70 km long-range Raman distributed optical fibre sensing through enhanced anti-distortion coding and waveform reconstruction

Domain: physics
Published: 2025-12-15
Editorial outcome: accept

Abstract
The practical implementation of Raman distributed optical fibre sensing has been fundamentally constrained by the inherent low signal-to-noise ratio (SNR), particularly for sensing distance exceeding 30 km. We propose a paradigm that combines enhanced anti-distortion coding processing, advanced Raman scattering waveform reconstruction preprocessing, and Haar wavelet denoising to transcend this physical limitation. The proposed pre-processing framework simultaneously optimises complementary sequences correlation, effectively mitigates disturbances of transient effects and improves sensing performance. The experimental demonstration achieves performance metrics: 70.0 km sensing distance with 1.58 m spatial resolution, while maintaining 0.91 °C measurement accuracy and 5.39 °C temperature resolution. The tripartite synergistic mechanism, consisting of the waveform reconstruction pre-processing framework compensating for and suppressing transient effects, coding gain improving the baseline SNR, and the Haar wavelet transform removing residual noise, breaks through the theoretical trade-off constraint between SNR and sensing distance in traditional schemes. The proposed approach demonstrates a potential for application in the fields of long-range infrastructure monitoring and environmental sensing.

Introduction
In 1928, physicist Raman C. V. published a paper titled A type of secondary radiation in Nature 1, and since then, the phenomenon of Raman scattering has been extensively and intensively studied. Over the past decades, Raman distributed optical fibre sensing has emerged as a research frontier 2–7, distinguished by its fast measurement speed, simple structure and inherent temperature sensitivity 8–11. It has been widely applied in safety monitoring of infrastructure systems, including transportation networks, power transmission facilities and large-scale linear installations, owing to its unique capability for continuous temperature measurement along the entire length of the sensing fibre 12–16. However, in contrast to Rayleigh and Brillouin scattering light 17, Raman scattering light exhibits lower intensity characteristics. Since the Raman scattering signal is 50 dB weaker than the incident detection signal 18,19, the Raman distributed optical fibre sensing has the technical bottleneck of lower SNR, which seriously hampers the advancement of long-sensing-distance applications. While increasing the pulse width effectively enhances the SNR of Raman scattering signal 20, this improvement occurs at the expense of degraded spatial resolution which creates a technical bottleneck that cannot balance the sensing distance and spatial resolution.

To address these challenges and increase the sensing distance, advanced SNR optimisation schemes, including algorithmic denoising schemes 21–24, neural network schemes 25,26 and pulse coding schemes 27–29, have been implemented in Raman distributed optical fibre sensing.

Algorithm denoising schemes aim to improve the SNR of the system by processing optical fibre scattering signals. For example, Yu et al. proposed a dynamic sampling-correction scheme achieving a sensing distance of 20.0 km 23. Pradhan et al. proposed a Fourier wavelet regularised deconvolution scheme achieving a sensing distance of 30.0 km with 3.0 m spatial resolution 24. Essentially derived from mathematical optimisation theory, such schemes only denoise signals from the perspective of signal processing without achieving breakthroughs in physical mechanisms. Furthermore, they have limitations, including parameter dependence and difficulty in preserving the true characteristics of signals 30.

In addition, as one of the current mainstream denoising methods, convolutional neural network scheme is a typical data-driven approaches. It optimises model parameters using large-scale training datasets, with the goal of achieving effective processing of test data. For example, Zhang et al. proposed a deep 1-D denoising convolutional neural network scheme, which realised a sensing distance of 10.0 km with a spatial resolution of 3.0 m 26. However, the performance of this method is significantly constrained by the specificity of training data. When there is a distribution difference between test signals and the training set, its effect on enhancing sensing performance will be limited.

Pulse coding schemes have demonstrated significant advantages in long-distance Raman distributed optical fibre sensing. On one hand, by encoding the detection optical pulses, this technology can significantly increase the optical power injected into the sensing fibre while avoiding fibre non-linear effects, thereby enhancing the intensity of effective sensing signals at the level of signal generation mechanism. On the other hand, at the data processing level, it leverages the separability between encoded signals and uncoded noise to effectively suppress noise and improve the SNR of system.

Currently, five typical pulse coding schemes are widely applied in Raman distributed optical fibre sensing, which specifically include the simplex coding scheme 31, low-repetition-rate cyclic pulse coding scheme 27, pre-shaped simplex coding scheme 32, genetic-optimised aperiodic coding scheme 29 and derived sequences coding scheme 33. For example, Park et al. achieved 37.0 km sensing distance, 17.0 m spatial resolution, 3.0 °C temperature resolution and 2176 effective sensing points via simplex coding scheme 31. Soto et al. achieved 26.0 km sensing distance, 1.0 m spatial resolution, 3.0 °C temperature resolution and 26,000 effective sensing points with a low-repetition-rate cyclic pulse coding scheme 27. Rosolem et al. achieved 62.0 km sensing distance, 10.0 m spatial resolution, 8.4 °C temperature resolution and 6200 effective sensing points using a pre-shaped simplex coding scheme 32. Sun et al. achieved 39.0 km sensing distance, 1.0 m spatial resolution, 3.9 °C temperature resolution and 39,000 effective sensing points based on a genetic-optimised aperiodic coding scheme 29. Chai et al. achieved 44.0 km sensing distance, 5.0 m spatial resolution, 2.5 °C temperature resolution and 8800 effective sensing points with a derived sequences coding scheme 33.

However, existing pulse coding schemes in Raman distributed optical fibre sensing remain constrained by several prevalent bottlenecks: high hardware implementation complexity, excessive computational overhead in encoding and decoding, limited non-linear effect suppression capability, and inadequate resistance to signal distortion coupled with poor stability during long-distance transmission. Collectively, these factors constrain the system’s application potential in high-performance scenarios, including low SNR environments and long-distance sensing applications.

To address the aforementioned limitations, this paper proposes an enhanced anti-distortion coding (EAD-coding) and waveform reconstruction scheme. Based on a tripartite synergistic mechanism, the proposed scheme effectively alleviates the conventional trade-offs among SNR, sensing distance and hardware cost. This mechanism integrates three key components: a pre-processing framework that compensates for transient effects in erbium-doped fibre amplifiers (EDFA), an encoding strategy that enhances the SNR of sensing signals through coding gain, and a refined residual noise suppression process based on the Haar wavelet transform. Experimental results demonstrate that the proposed scheme achieves a sensing distance of 70.0 km, a spatial resolution of 1.58 m, a temperature resolution of 5.39 °C, and a temperature measurement accuracy of 0.91 °C, with the number of effective sensing points reaching 44,303. To the best of our knowledge, this value represents the highest number of effective sensing points reported to date in the field of Raman distributed optical fibre sensing. Furthermore, while maintaining relatively low complexity, the EAD-coding scheme improves the system’s anti-distortion capability and operational adaptability, offering a solution for long-distance Raman distributed fibre sensing.

Results
Experimental setup
We built a Raman distributed optical fibre sensing experimental setup based on proposed EAD-coding and waveform reconstruction scheme, as shown in Fig. 1. Firstly, the laser device generates continuous laser with a central wavelength of 1550 nm, and then the encoded detection signals based on Golay complementary sequences are generated by using the digital delayed pulse generator (DDPG) to modulate the semiconductor optical amplifier (SOA). Each detection signal is amplified by EDFA and then enters a single-mode sensing fibre through a wavelength division multiplexer (WDM), and generates Raman backscattered signal (RBS) which enters an avalanche photo-detector (APD) for amplification and optoelectronic conversion. Finally, all RBSs generated by detection signals are collected by a data acquisition card (DAC) and demodulated in a computer to obtain the distributed temperature information.

In this study, Golay complementary sequences are applied in Raman distributed optical fibre sensing, and an enhanced anti-distortion coding scheme is developed based on these sequences. Fig. 2 presents the flowchart of the EAD-coding scheme, detailing its encoding and decoding processes, demodulation and localisation principles and signal waveform reconstruction framework.

Figure 2a shows the encoding principle. Its main function is to produce four complementary optical detection signals after convolution with a single-pulse signal. After being amplified by the EDFA, the waveforms of these four channels of detection signals will undergo distortion, as shown in Fig. 2b. Then these distorted detection signals enter the sensing fibre and generate RBSs, as shown in Fig. 2c. These RBSs will be analyzed and reconstructed to recover the autocorrelation in process of decoding, as shown in Fig. 2d. Finally, the distributed temperature information is demodulated, as shown in Fig. 2e.

The detailed principles of the pre-processing procedure are presented in the ‘Method’ section, and the specific principles of the EAD-coding and waveform reconstruction scheme are described in the Supplementary Information.

Impact of transient effects on the detection signals and RBSs
In Raman distributed optical fibre sensing, the transient effects impact the sensing performance (SNR and temperature accuracy). Transient gain fluctuations in an EDFA arise because the relaxation process of the population inversion cannot equilibrate instantaneously with rapid changes in the input laser power. This phenomenon will lead to a non-uniform amplification that the detection signals will distort in timing when passing through the EDFA, thereby disrupting the autocorrelation of the detection signals and ultimately limiting the system’s sensing performance.

The proposed scheme generates four sets of correlated detection signals (u(n), u'(n), w(n), w'(n), then denotes the discrete point) based on the EAD-coding approach. In the experiment, we first characterise the detection signals and evaluate the influence of transient effects. These detection signals are acquired before and after the EDFA for timing analysis, as shown in Fig. 3a–d and all curves are normalised to ensure consistency in comparative analysis. The yellow curves are the detection signals affected by transient effects, and the blue curves are the detection signals that are not affected by transient effects. It can be clearly seen that the transient effects cause the gain of EDFA to be non-uniform. These detection signals show a gradual decay trend in the timing after passing through EDFA, which results in a weakening of autocorrelation. Ultimately, the distortion in the detection signals adversely affect the overall sensing performance of the system.

To validate the impact of transient effects on autocorrelation characteristics, we conducted an analysis experiment of the autocorrelation curves before and after the transient effects. The blue curve in Fig. 3e is the autocorrelation function before transient effects. As clearly shown, the autocorrelation curve exhibits a standard unit impulse function (Dirac delta function) profile with no discernible sidelobe noise adjacent to the main peak, demonstrating a better autocorrelation characteristic. As shown in Fig. 3f, pronounced sidelobe noise emerges on both sides of the autocorrelation main peak, evidencing degradation of autocorrelation characteristics under transient effects.

The degradation of autocorrelation characteristics induced by transient effects significantly compromises the system’s sensing performance. To systematically investigate the impact of transient effects on sensing performance, we conducted a quantitative analysis experiment on both the RBSs generated from four detection signals after transient effects and their corresponding decoding results. We also conducted a comparative analysis experiment of the waveform reconstructed RBSs and their corresponding decoded results based on EAD-coding and the waveform reconstruction scheme. Quantitative analysis in Fig. 4 reveals that transient effects will lead to the weakening of the RBSs intensity generated by these distorted detection signals, as shown by the yellow curves in Fig. 4a–d, thereby decreasing SNR of the system. The waveform reconstruction (pre-processing) effectively suppresses transient effects, yielding an average SNR enhancement of 1.11 dB (the average SNR improvement of the RBSs generated by the aforementioned four detection signals) as depicted by the blue curves. Theoretically, the greater the influence of transient effects, the more pronounced the intensity enhancement of RBSs in the pre-processing within the EAD-coding scheme. In addition, all curves are normalised to ensure comparative analysis consistency.

Transient effects not only reduce the intensity of RBSs generated by these detection signals but also lead to the weakening of the decoded RBS, as shown in Fig. 4e. The decoded results prior to and following pre-processing are depicted by the yellow and blue curves, respectively. The result demonstrates that the decoded RBS intensity after pre-processing exhibits a higher magnitude compared to the intensity before pre-processing, thereby confirming a suppression of transient effects. To investigate the impact of transient effects on decoding performance, we systematically calculated the corresponding SNR. Due to the detrimental impact of transient effects on decoding fidelity, the reduced intensity of decoded RBSs consequently degrades the SNR. The EAD-coding and waveform reconstruction scheme effectively suppress transient perturbations, restoring the decoded RBS intensity and thereby enhancing SNR by 1.45 dB, which experimentally validates the effectiveness of the EAD-coding and waveform reconstruction scheme.

Furthermore, an autocorrelation analysis is performed on the pre-processed detection signals coupled into the sensing fibre to confirm their efficacy in eliminating transient effects. The primary objective of this experiment is to verify that the waveform reconstructed RBSs are equivalent to the RBSs of the undistorted detection signals. Taking the detection signal u(n) as an example, the detection signal coupled into the sensing fibre after waveform reconstruction can be calculated and is given by Eq. (1).

u0(n) = ifft(fft[uf(n)] / fft[f01(n)]) (1)

In Eq. (1), u'(n) is the equivalent detection signal after reconstruction of u(n). f01(n) is the transient-modulated function of u(n). The uf(n) represents the detection signal u(n) after it has been subjected to transient effects. Where fft is the Fourier transform operation, ifft is the inverse Fourier transform operation. Then, we performed the same processing on the four detection signals and conducted autocorrelation operations on the processed detection signals. When Eq. (2) holds true, the results demonstrate that the autocorrelation characteristics are restored after waveform reconstruction, accompanied by the suppression of transient effects. In Eq. (2), signals u0(n), u'0(n), w0(n), w'0(n) are the equivalent detection signals obtained from the waveform reconstruction of signals u(n), u'(n), w(n), w'(n). The * denotes the corresponding operation. l is code length. δ(n) is a unit impulse function (Dirac delta function).

[u0(n) * u0(n)] + [u'0(n) * u'0(n)] + [w0(n) * w0(n)] + [w'0(n) * w'0(n)] = 2lδ(n) (2)

The experimental results are shown in Fig. 4g, h. Figure 4g presents the autocorrelation function curve of the detection signals with waveform distortion caused by transient effects. And Fig. 4h shows the autocorrelation function of the equivalent detection signals coupled into the sensing fibre after pre-processing. It can be clearly observed that the sidelobe noise of the autocorrelation function curve is significantly reduced, which verifies that the autocorrelation characteristics are restored and the transient effects are suppressed.

RBS denoising and SNR enhancement
In this study, a synergistic approach that integrates EAD-coding with Haar wavelet denoising is applied to suppress temperature fluctuation noise along the sensing optical fibre. Based on the EAD-coding scheme, the incident optical power can be substantially increased without inducing stimulated Raman scattering, leading to enhanced effective Raman signal intensity. Furthermore, the separability between encoded signals and uncoded noise enables effective noise suppression, resulting in an improved SNR. Among them, a denoising method based on the Haar wavelet is adopted to process distributed temperature sensing signals with abrupt change characteristics. Owing to its inherently step-like structure, the Haar wavelet is well-suited for extracting features from signal singularities, particularly in regions of abrupt temperature change along the sensing fibre. The Haar wavelet function generates a set of orthogonal basis functions through translation and scaling, enabling multi-scale decomposition of signals. Its inherent advantage in processing low-complexity signals with abrupt change characteristics makes it particularly suitable for the analysis of RBSs.

To improve the SNR performance, we adopted a 6-level Haar wavelet. In addition, in the post-processing stage of temperature demodulation, to further suppress noise and enhance signal smoothness, we additionally applied the db10 (Daubechies wavelet 10) wavelet function with 4-level decomposition. It should be noted that while this step improves signal quality (by reducing temperature fluctuation), it moderately degrades the spatial resolution of the system. Such parameter adjustment reflects the necessary trade-off between spatial resolution and temperature measurement accuracy.

To validate the performance improvement achieved by the synergistic approach that integrates EAD-coding with Haar wavelet denoising, we further compare the decoded RBS intensity based on the EAD-coding scheme with the conventional single-pulse scheme, as shown in Fig. 5a. The EAD-coding scheme exhibits a higher Raman gain, which results in a stronger signal intensity compared to the conventional single-pulse demodulation scheme. As shown in Fig. 5b, c the Haar wavelet is implemented for further denoising to enhance SNR of Raman distributed optical fibre sensing. It could be clearly seen that the EAD-coding scheme (with Haar wavelet) achieves a reduction in peak-to-peak ratio from 0.0081 to 0.0006 at the end of the sensing fibre, which will substantially extend the sensing distance of the system. Furthermore, Fig. 5b corroborates that the Haar wavelet provides consistently effective noise suppression in the single-pulse demodulation scheme. The conventional single-pulse scheme (with Haar wavelet) achieves a reduction in peak-to-peak ratio from 0.013 to 0.0011 at the end of the sensing fibre.

As shown in Fig. 5d, e, the Haar wavelet function significantly improves the SNR for both the EAD-coding scheme and the conventional single-pulse scheme. Experimental results indicate that after Haar wavelet denoising, the SNR of the EAD-coding scheme and the conventional single-pulse demodulation scheme is increased by 7.63 dB and 2.92 dB, respectively. It is worth noting that a relatively significant difference emerges between the two demodulation schemes at the end of the sensing fibre. For the single-pulse scheme, the effective Raman scattering signal is basically submerged by system noise beyond 42.0 km. After incorporating the Haar wavelet function, although the noise level is reduced, the RBS is still submerged by noise beyond 56.0 km. Therefore, the improvement in SNR at the end of the sensing fibre is relatively limited for the single-pulse scheme. This also confirms that the wavelet denoising algorithm has a limited capability to improve SNR in long-distance distributed optical fibre sensing demodulation schemes. Hence, we combine the EAD-coding scheme with Haar wavelet denoising. Only by avoiding the effective Raman scattering signal being submerged by system noise as much as possible can the wavelet denoising algorithm maximise the SNR of the sensing signal.

Enhancement of temperature sensing performance
The temperature demodulation and SNR results are shown in Fig. 6a shows that the conventional single-pulse scheme exhibit substantial temperature fluctuations on the order of 300 °C. The synergistic approach that integrates EAD-coding with Haar wavelet denoising significantly reduces the system’s temperature fluctuation to 22.51 °C while improving the SNR by 7.24 dB (compared to conventional single-pulse scheme), as shown in Fig. 6b, e. Furthermore, the pre-processing architecture within EAD-coding further reduces the system’s temperature fluctuation to 20.86 °C by suppressing transient effects and reconstructing RBSs, as shown in Fig. 6c. Meanwhile, the SNR is further improved by an additional 1.48 dB, as shown in Fig. 6f. Temperature fluctuation is expressed as the difference between the measured temperature and the room temperature. Specifically, in Raman distributed optical fibre sensing system, there is a discrepancy between the demodulated temperature (T’) at the sampling points of the sensing fibre and the room reference temperature (T₀). This discrepancy is defined as temperature fluctuation (ΔT = T’ − T₀).

Temperature resolution refers to temperature uncertainty, which characterises the system’s ability to distinguish temperature changes, and is generally defined as the standard deviation (σ) of measured temperatures under constant temperature conditions 34,35. In this experiment, temperature resolution is characterised by the temperature standard deviation of each distributed temperature measurement point within a fixed length of the sensing fibre. Compared with the temperature resolution of 29.25 °C achieved by the conventional single-pulse scheme, synergistic approach that integrates EAD-coding with Haar wavelet denoising improves the system’s temperature resolution to 5.82 °C, as shown in Fig. 6h. Meanwhile, the pre-processing architecture within EAD-coding further enhances the system’s temperature resolution to 5.39 °C by suppressing transient effects and reconstructing RBSs, as shown in Fig. 6i. Experimental results show that at a sensing distance of 70.0 km, the EAD-coding and waveform reconstruction scheme achieves a temperature resolution that is 5.43 times better than the conventional method.

Meanwhile, we further compared the temperature measurement accuracy performance of the system, as shown in Fig. 6j–l. The transient effects adversely impact key performance, including the SNR, temperature fluctuation, temperature resolution, and also compromise the overall temperature measurement accuracy of the system. Under the experimental condition of a 90 °C FUT (fibre under test) temperature. The experimental results show that the demodulated temperature of the distorted signal before pre-processing is 104.98 °C, with a maximum measurement deviation of 14.98 °C. As the temperature rises, the elevation of the Raman backscattered curve in the FUT becomes more pronounced, and temperature measurement deviation gradually increases as well (from 3.08 °C in Fig. 6i to 14.98 °C in Fig. 6l). Consequently, the temperature measurement accuracy deteriorates accordingly. After pre-processing architecture, the temperature demodulation result is 90.91 °C, and the temperature measurement accuracy is 0.91 °C, representing an improvement of approximately 16.46 times. Therefore, the EAD-coding and waveform reconstruction scheme can effectively improve the temperature measurement accuracy of the long-distance Raman distributed optical fibre sensing system (with a sensing distance of 70.0 km) to within 1.0 °C.

The spatial resolution measurement result is presented in Fig. 7, which demonstrates the precise identification of both the spatial position and length of FUT. This experiment achieves a spatial resolution of 1.58 m. It confirms the effectiveness of the demodulation principle of EAD-coding and the waveform reconstruction scheme. In this scheme, the pulse width of a single code element is set to 10 ns, corresponding to a theoretical spatial resolution of 1.0 m. The application of wavelet denoising filters out the temperature envelope information in the FUT, resulting in an experimental spatial resolution that is lower than the theoretical value.

Above all, through the EAD-coding, Haar wavelet denoising and waveform reconstruction scheme, the theoretical trade-off bottleneck between SNR and sensing distance in traditional schemes is broken while maintaining relatively low complexity. Experimental results demonstrate that at a long distance of 70.0 km, the system achieves a temperature resolution of 5.39 °C. Moreover, the pre-processing architecture in EAD-coding (integrating autocorrelation characteristic analysis of RBSs and waveform analysis and reconstruction) enhances the temporal fidelity and transmission stability of encoded pulse sequences. This further improves the system’s SNR and temperature measurement accuracy, enabling the temperature measurement accuracy to reach 0.91 °C. In this study, the improvements in SNR (accompanied by performance enhancements in sensing distance and temperature resolution) are primarily attributed to the proposed EAD-coding (for coding gain compensation) and Haar wavelet denoising schemes. In contrast, the pre-processing architecture within EAD-coding serves to improve the system’s temperature measurement accuracy by suppressing transient effects and reconstructing RBSs.

Methods
In Raman distributed optical fibre sensing system, higher incident optical power corresponds to an improved SNR. Consequently, amplification of the incident light is typically implemented using EDFA. However, the transient effects of EDFA can significantly degrade sensing performance. This phenomenon induces non-uniform amplification, leading to waveform distortion of the encoded pulse after passing through the EDFA. It manifests as a gradual attenuation profile in timing, which disrupts the autocorrelation properties of the encoded pulse. Consequently, the system experiences both a degraded SNR and a constrained maximum sensing distance. The functional representation of this distortion mechanism is formally defined in Eq. (3).

uf(n) = u(n) * f1(n) (3)

Where uf(n) is the encoded pulse u(n) amplified by the EDFA, and f1(n) is the attenuation envelope induced by transient effects. The transient effects inherent to EDFA critically distort the waveform of encoded signals, compromising their integrity in correlation-based sensing systems. The intensity of the RBS generated by the signal uf(n) is governed by the relationship expressed in Eq. (4).

Iu(n) = [u(n) * f1(n)] ⊗ hk(n) (4)

Where Iu(n) is the RBS intensity produced by uf(n), hk(n) is the pulse response in Raman distributed fibre optical sensing system. The ⊗ denotes the convolution operation.

As demonstrated by Eq. (4), all four segments of the acquired RBSs are subjected to transient effects, resulting in attenuation of the backscattered intensity. To mitigate transient effects, a pre-processing scheme is implemented for RBSs. This involves analyzing the distorted signals and reconstructing their waveforms, thereby restoring the autocorrelation properties compromised by transient effects. The attenuation envelope induced by EDFA transient effects is reformulated from a multiplicative operation to a convolutional operation; the RBS is mathematically formulated as shown in the following equation:

Iu(n) = u(n) ⊗ f01(n) ⊗ hk(n) (5)

Where f01(n) is the transient-modulated function. This function does not require an explicit analytical definition, as its functional form is fully determined by the attenuation envelope f1(n), as formalised in the following equation:

f01(n) = ifft(fft[u(n) * f1(n)] / U(k)) (6)

Where fft is the Fourier transform operation, ifft is the inverse Fourier transform operation, U(k) is the Fourier transform result of u(n), k denotes the discrete frequency. It should be noted that u(n) * f1(n) denotes the timing of the normalised detected signal collected at the output port of the EDFA, and u(n) denotes the timing of the normalised detected signal collected at the output port of the SOA. The RBS in Eq. (7) is subjected to Fourier transform processing, as mathematically expressed in the following equation:

fft[Iu(n)] = U(k) * F01(k) * Hk(k) (7)

Where the Fourier transform results of the encoded pulse u(n), the transient-modulated function f01(n) and pulse response hk(n) are represented by U(k), F01(k) and Hk(k). The waveform reconstructed RBS through inverse Fourier transform processing is mathematically formulated in Eq. (8). In Eq. (8), I0u(n) is the waveform reconstructed RBS intensity.

I0u(n) = ifft(fft[Iu(n)] / F01(k)) = u(n) ⊗ hk(n) (8)

For the encoded pulse u(n), the RBS intensity (unaffected by transient effects) generated is mathematically expressed through Eq. (9). In Eq. (9), I(n) is the RBS intensity produced by u(n).

I(n) = u(n) ⊗ hk(n) (9)

Comparison of Eq. (8) with Eq. (9) reveal that the transient effects in the RBS are fully eliminated after waveform reconstruction. The autocorrelation properties can be recovered by implementing the same pre-processing protocol on the remaining three RBSs.

The pre-processing architecture within the EAD-coding and waveform reconstruction scheme incorporates autocorrelation characteristic analysis, waveform analysis and reconstruction of RBSs. It can suppress the transient effects introduced by EDFA, thereby significantly improving the amplitude fidelity and temporal stability of the encoded pulse sequence. This innovative active reconstruction mechanism in the signal domain, which is based on analyzing the waveforms of RBSs via forward/inverse Fourier transform, directly eliminates the phenomenon of detection pulse distortion existing in traditional demodulation schemes. The scope of action of the pre-processing architecture encompasses two key aspects: specifically, one is addressing the fundamental limitation of detection signal distortion through physical-layer waveform reconstruction, and the other is reconstructing RBSs to restore the ideal autocorrelation characteristics of encoded sequences, and achieve a theoretical gain value, thereby achieving the coordinated optimisation of waveform correction, autocorrelation characteristic restoration and signal intensity enhancement.

Furthermore, the proposed EAD-coding and waveform reconstruction scheme features a synergistically enhanced two-stage noise suppression mechanism, demonstrating innovations in multi-level joint denoising.

First, this scheme enhances the SNR of sensing signals through its inherent coding gain. Based on the autocorrelation characteristics of its sequence design, this scheme provides an inherent gain, which effectively improves the system’s baseline SNR. Furthermore, this mechanism not only significantly boosts optical power but also leverages the irrelevance between the encoded signals and uncoded noise to achieve preliminary suppression of SNR at the encoding-decoding level.

Second, aiming at the residual noise with specific time-frequency domain distribution characteristics in the decoded signals, this scheme further introduces the Haar wavelet transform for adaptive noise filtering. The multi-resolution analysis capability of the Haar wavelet enables accurate capture of the local time-frequency features of noise. By performing sparse representation of the signal at different scales (corresponding to different frequency bands) and time-domain positions, it achieves effective separation between useful signals and non-stationary noise components. While preserving the key details of the distributed temperature signal, this method efficiently eliminates residual noise, significantly enhancing the clarity of the signal in the time-frequency domain and the overall measurement accuracy of the system.

This three-fold synergistic mechanism, consisting of the pre-processing framework compensating for suppressing transient effects, coding gain improves baseline SNR, and wavelet transform finely removing residual noise, breaks through the theoretical trade-off bottleneck between SNR and sensing distance in traditional schemes. This scheme provides a framework for long-distance Raman distributed optical fibre sensing. Experimental results indicate that, at a long distance of 70.0 km, this scheme can achieve a spatial resolution of 1.58 m, a temperature resolution of 5.39 °C, a measurement accuracy of 0.91 °C, and an effective number of sensing points reaching 44,303. To the best of our knowledge, the effective number of sensing points of the EAD-coding and waveform reconstruction scheme currently represent the world’s highest level in the field of Raman distributed optical fibre sensing.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors present a novel manuscript discussing a long-range Raman distributed optical fiber sensing scheme through\nGolay-encoded autocorrelation and waveform reconstruction technology. The practical implementation of Raman-based\ndistributed optical fiber sensing has been fundamentally constrained by the inherent low signal-to-noise ratio, particularly for\noperational ranges exceeding 30 km. The authors propose a groundbreaking paradigm integrating Golay-encoded\nautocorrelation processing with advanced Raman scattering waveform reconstruction to transcend this physical limitation.\nAnd the newly developed preprocessing framework simultaneously optimizes complementary sequence correlation and\neffectively mitigates disturbances of transient effects. The experimental results demonstrate a sensing performance of 70 km\noperational range with 1.58 m spatial resolution, while maintaining 0.88 °C measurement accuracy. To my knowledge, this\nrepresents the first work in achieving such a long sensing distance with 1 meter-level spatial resolution. The manuscript can\nbe accepted if the following comments are addressed:\n(1) In Raman distributed temperature sensing systems, spatial resolution is intrinsically determined by the probing pulse\nduration, as the pulse width directly defines the minimum spatial discrimination through time-of-flight measurements. The\npaper explicitly states that the pulse width of a single code element is set to 10 ns and single-mode fiber is employed to\navoid spatial resolution degradation due to intermodal dispersion. However, the experimental results show that the achieved\nspatial resolution failed to reach the theoretical spatial resolution of 1 m. What is the reason for the different between\ntheoretical prediction and experimental outcome?\n(2) The method mentioned in this paper only explores the effect of the transient effect on anti-Stokes light in analyzing the\ntransient effect. And only the anti-Stokes light is used in the temperature demodulation process, discarding the use of Stokes\nsignals. How does this differ from the traditional dual-channel demodulation scheme that relies on both anti-Stokes and\nStokes signals, and what are its significant advantages?\n(3) The experimental setup section lacks detailed descriptions of the specific types and parameters for each device, which\nmay hinder readers from reproducing the experiment. It is advisable to supplement the detailed specifications of the optical\ncomponents used, including their models, manufacturers, and key optical parameters.\n(4) In this paper, the Raman backscattered signals are analyzed by calculating the SNR in Fig. 4, whereas only peak-to-\npeak values are compared in the wavelet denoising results presented in Fig. 5. It is recommended to include a SNR\nanalysis to ensure consistency in evaluation metrics across different experimental analyses.\n(5) This paper only compares the EAC-coding scheme with the traditional single pulse scheme in the experiment, which\nhinders the demonstration of its superiority. It is recommended to include a table in the discussion section detailing the\nperformance metrics and comparative advantages/disadvantages of various mainstream techniques, thereby highlighting\nthe superiority of this study.\n(6) The paper clearly states that the acquisition time for each Raman scattering signal is 63 minutes, and a total of four\nRaman scattering signals need to be acquired during the decoding stage. Given the prolonged acquisition duration, how is\nthe stability of the experimental temperature and optical instruments performance ensured?\n(7) Discrepancies in typography consistency are observed in Fig. 3-Fig. 7, particularly regarding the font sizes of axis\ncaptions and intra-figure text. For example, the axis labels in Fig. 6-Fig. 7 and the text in Fig. 7(b) exhibit notably larger font\nsizes compared to other figures. It is recommended to standardize the typography across all figures to ensure visual\ncoherence and readability.\n(8) Some of the chart labels are not clear enough. For example, the text in Fig. 2 is undersized and the color contrast is\ninsufficient, while the caption text in Fig. 3(b) appears blurred. It is recommended that the format and size of all figures be\nstandardized to improve visual clarity and ensure that labels and annotations are clear and easy to read and consistent\nthroughout the manuscript.", "reviewer_2": "The authors have demonstrated a record-long-distance distributed temperature sensing system based on Raman scattering.\nBy combining Golay-encode autocorrelation processing, EDFA-transient-effect mitigation, and Haar wavelet denoising, the\nperformance of the sensing system has been significantly enhanced, achieving 1.58m spatial resolution and 0.88 °C\nmeasurement accuracy at a maximum sensing range of 70km. This work represents a solid engineering breakthrough in\nlong-distance distributed temperature sensing and has the potential to generate societal impacts by providing new\ncapabilities to infrastructure monitoring. Therefore, this manuscript can be accepted after being further improved by\naddressing the specific comments below.\n1. The introduction should be significantly optimized to clearly state the key innovation of this work. For example, the authors\nmentioned several existing denoising techniques, but their limitations and the corresponding advantages of Haar wavelet\ndenoising is not mentioned at all.\n2. As the core innovation of this work, the uniqueness of Golay-encode autocorrelation processing is insufficiently explained.\nHow does it compare quantitatively to other well established coding methods such as Simplex coding and genetic-optimized\naperiodic coding? For example, maybe the discussion can be made from the perspective of coding gain and measurement\ntime. After all, the physical reason that the record-breaking performance can be achieved should be explicitly pointed out.\n3. To let the reader to better evaluate the performance in this work, a quantitative and fair comparison with the state of the art\nshould be made. If possible, a figure of merit should be given that normalizes the measurement time, considering that the\nperformance in this work is obtained over one hour.\n4. More in-depth discussions should be provided to talk about the physical limit of current performance and potential ways\nfor further enhancement.\n5. Details of Haar wavelet denoising should be provided. How is it implemented? Does it sacrifice spatial resolution?\n6. It is confusing why the temperature-measurement uncertainty can be much larger than the resolution.\n7. Some minor mistakes should be revised. For example, peak-to-peak ratio from 0.0067 to 0.0006 should be attributed to\nHaar wavelet denoising instead of to EAC-coding. Results for the single-pulse scheme are shown in Fig. 5(b1) instead of\nFig. 5(b2).", "reviewer_3": "Responds to the reviewers’ comments:\nReviewer 2 (Comments to the Author):\nRecommendations for the Author(s):\nThe authors have demonstrated a record-long-distance distributed temperature sensing\nsystem based on Raman scattering. By combining Golay-encode autocorrelation\nprocessing, EDFA-transient-effect mitigation, and Haar wavelet denoising, the\nperformance of the sensing system has been significantly enhanced, achieving 1.58m\nspatial resolution and 0.88℃ measurement accuracy at a maximum sensing range of\n70km.This work represents a solid engineering breakthrough in long-distance\ndistributed temperature sensing and has the potential to generate societal impacts by\nproviding new capabilities to infrastructure monitoring. Therefore, this manuscript\ncan be accepted after being further improved by addressing the specific comments\nbelow.\n\nReply: Thank you very much for your evaluation of the content of this\nresearch and your constructive suggestions on the manuscript. We are also\nvery grateful to the reviewers for their recognition of the innovation of the\nproposal presented in this manuscript. These comments are of great value and\nwill be very helpful for revising and improving the manuscript as well as\nguiding the research work. We have carefully studied your comments and\nmade revisions accordingly, hoping that the revised version will meet your\nrequirements.\n\n1. The introduction should be significantly optimized to clearly state the key\ninnovation of this work. For example, the authors mentioned several existing\ndenoising techniques, but their limitations and the corresponding advantages of Haar\nwavelet denoising is not mentioned at all.\n\nReply: Thank you very much for the valuable and professional\ncomments from the reviewers, we fully concur with the reviewer's comments.\nBased on the reviewer's professional suggestions, we have made substantial\nrevisions to the introduction section, and three parts of revisions have been\nmade in the revised manuscript. First, we have supplemented the discussion\non the limitations of existing technologies in the Introduction and Discussion\nsection. Second, we have added content regarding the innovativeness of the\nEAC-coding technique in the last paragraph of the Introduction. Finally, we\nhave included the advantages of Haar wavelets in the Experimental Results\nsection. The specific supplementary content in the revised manuscript is as\nfollows.\n(1) Based on the professional suggestions of the reviewer, we have\nsupplemented the discussion on the limitations of existing technologies in\nthe Introduction and Discussion section. The specific supplementary\ncontent is as follows.\nAlgorithm denoising schemes aim to improve the SNR of the system by\nprocessing optical fiber scattering signals. Essentially derived from\nmathematical optimization theory, such schemes only denoise signals from\nthe perspective of signal processing without achieving breakthroughs in\nphysical mechanisms. Furthermore, they have limitations including\nparameter dependence and difficulty in preserving the true characteristics of\nsignals [1]. In addition, as one of the current mainstream denoising methods,\nconvolutional neural networks (CNNs) scheme is a typical data-driven\napproach. It optimizes model parameters using large-scale training datasets,\nwith the goal of achieving effective processing of test data. However, the\nperformance of this method is significantly constrained by the specificity of\ntraining data; when there is a notable distribution difference between test\nsignals and the training set, its effect on enhancing sensing performance will\nbe limited.\nIn contrast, pulse coding technology exhibits unique advantages in\nlong-distance Raman distributed optical fiber sensing, with its strengths lying\nin two aspects: physical mechanisms and information processing. At the\nphysical mechanism level, by encoding and modulating the detection optical\npulses, this technology significantly increases the optical power injected into\nthe sensing fiber without inducing fiber nonlinear effects, thereby enhancing\nthe intensity of the excited Raman scattering signals at the physical source [2].\nAt the signal processing level, pulse coding technology fully leverages the\nseparability between coded signals and background noise in the\ntime/frequency domain. Through matched filtering or demodulation\nalgorithms, it achieves effective noise suppression, thus improving the SNR\nat the signal processing level [3].\nCurrently, the pulse coding techniques applied in Raman distributed\noptical fiber sensing system mainly include the following: Simplex coding\nscheme, Pre-Shaped Simplex coding scheme, Low-repetition-rate cyclic\npulse coding scheme, Genetic-optimised aperiodic coding scheme, and\nDerived Sequences coding scheme. Their key performance indicators are\npresented in Table 2. Simplex coding scheme is a linear coding technique\nbased on Hadamard matrix transformation, where its code length (L bits) determines the number of detection signal groups required (L groups) [4]. The\nmain limitation of this scheme lies in the linear growth of data acquisition\nvolume and computational complexity with code length, which restricts its\npractical efficiency in applications requiring long code lengths and\nhigh-speed sensing. Low-repetition-rate cyclic pulse coding scheme\nutilizes an acousto-optic modulator (AOM) to generate Simplex\ncoding-based cyclic pulse sequences, enabling pulse injection at a low\nrepetition rate. This facilitates the injection of more energy into the sensing\nfiber, thereby enhancing the intensity of backscattered signals [2]. However,\nhigher pulse energy also makes it more likely to induce fiber nonlinear\neffects, and when approaching the stimulated scattering threshold, it restricts\nthe system’s sensing distance and SNR performance. Pre-Shaped Simplex\ncoding scheme introduces linear profile shaping of pulse amplitude based on\nthe Simplex code to compensate for the amplitude fluctuation of pulses\ncaused by EDFA, thereby improving system stability [5]. Although this\nscheme effectively suppresses the transient response of the EDFA at the\nhardware level, its hardware structure is more complex, leading to a\nsignificant increase in implementation cost. Genetic-optimised aperiodic\ncoding scheme generates aperiodic sequences (GO-code) through\noptimization via a distributed genetic algorithm (DGA), which are then\nconverted into optical pulse sequences and injected into the sensing fiber [3].\nThe core challenge of this scheme lies in its high dependence on optimization\nalgorithms to search for the optimal code, which typically requires\nsubstantial computational resources and iterative testing. Derived Sequences\ncoding scheme suppresses the impact of EDFA transient effects on\nlong-distance sensing by introducing a specific derived decoding strategy [6].\nHowever, its decoding process imposes a heavy computational burden, and\nthe core algorithm involves high-complexity matrix operations, making it\ndifficult to meet real-time requirements.\nCurrently, existing pulse coding techniques in Raman distributed optical\nfiber sensing remain constrained by several prevalent bottlenecks: high\nhardware implementation complexity, excessive computational overhead in\nencoding and decoding, limited nonlinear effect suppression capability, and\ninadequate resistance to signal distortion coupled with poor stability during\nlong-distance transmission. Collectively, these factors constrain the system’s\napplication potential in high-performance scenarios—including low\nSNR environments and long-distance sensing applications.\nTo address the aforementioned issues, an Enhanced anti-distortion\ncoding (EAC-coding) scheme is proposed in this manuscript. This scheme\neffectively overcomes the trade-off dilemma among SNR, sensing distance,\nand hardware cost in traditional methods through a three-fold synergistic\nmechanism: compensating for EDFA fluctuation via a preprocessing\nframework, suppressing transmission losses through coding gain, and finely\nremoving residual noise using wavelet transform. While maintaining\nrelatively low complexity, the EAC-coding scheme significantly enhances\nthe anti-distortion capability and adaptability of the system, providing a\nnew solution for long-distance, high-performance Raman distributed optical fiber\nsensing.\nTable 2. Sensing performance of various coding schemes.\n(2) Based on the professional suggestions of the reviewer, we have\nadded content regarding the innovativeness of the EAC-coding\ntechnique in the Introduction section. The specific supplementary\ncontent is as follows.\nEAC-coding scheme proposed in this manuscript incorporates a novel\npreprocessing framework for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered signals. The\npreprocessing architecture for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction in this scheme can effectively suppress\nthe transient effects introduced by EDFA, thereby significantly improving the\namplitude fidelity and temporal stability of the encoded pulse sequence. This\ninnovative active reconstruction mechanism in the signal domain, which is\nbased on analyzing the waveforms of Raman backscattered signals via\nforward/inverse Fourier transforms, directly eliminates the phenomenon of\ndetection pulse distortion existing in traditional demodulation schemes. The\nscope of action of the EAC-coding scheme encompasses two key aspects:\nspecifically, one is addressing the fundamental limitation of detection signal\ndistortion through physical-layer waveform reconstruction, and the other is\nperforming correlation operations between the proposed coding sequence and\nthe reconstructed Raman signal to restore the ideal cross-correlation\ncharacteristics of Golay sequences, and achieve a theoretical gain value,\nthereby breaking through the SNR-distance trade-off limit. It achieves the\ncoordinated optimization of “waveform correction, correlation characteristic\nrestoration, signal intensity enhancement”, laying a physical layer foundation\nfor long-distance sensing.\nFurthermore, the proposed EAC-coding scheme features a\nsynergistically enhanced two-stage noise suppression mechanism,\ndemonstrating innovations in multi-level joint denoising.\nFirst, EAC-coding scheme enhances the SNR of sensing signals through\nits inherent coding gain. Based on the cross-correlation characteristics of its\nsequence design, this coding scheme provides a significant inherent gain,\nwhich compensates for signal attenuation caused by long-distance\ntransmission and effectively improves the system's baseline SNR.\nFurthermore, this mechanism not only significantly boosts optical power but\nalso leverages the irrelevance between the decoding algorithm and incoherent\nnoise to achieve preliminary suppression of transmission link losses at the\nencoding-decoding level.\nSecond, aiming at the residual noise with specific time-frequency\ndomain distribution characteristics in the decoded signal, this scheme further\nintroduces Haar wavelet transform for adaptive noise filtering. The\nmulti-resolution analysis capability of the Haar wavelet enables accurate\ncapture of the local time-frequency features of noise. By performing sparse\nrepresentation of the signal at different scales (corresponding to different\nfrequency bands) and time-domain positions, it achieves effective separation\nbetween useful signals and non-stationary noise components. While\npreserving the key details of the distributed temperature signal, this method\nefficiently eliminates residual noise, significantly enhancing the clarity of the\nsignal in the time-frequency domain and the overall measurement accuracy\nof the system.\nThis three-fold synergistic mechanism, consisting of the\npreprocessing framework compensating for EDFA fluctuation, coding gain\nsuppressing transmission losses, and wavelet transform finely removing\nresidual noise, systematically breaks through the bottlenecks of traditional\nschemes in terms of SNR and sensing distance, providing a novel decoding\nframework for long-distance and high-precision Raman distributed optical fiber\nsensing.\n(3) Based on the professional suggestions of the reviewer, we have\nincluded the advantages of Haar wavelets in the Experimental Results\nsection. The specific supplementary content is as follows.\nIn this study, a denoising algorithm based on the Haar wavelet is\nadopted to process distributed temperature sensing signals with abrupt\nchange characteristics. The inherent step-like form of the Haar wavelet basis\nfunction endows it with excellent feature extraction capability for singular\npoints in the signal, especially for the abrupt temperature field change\nregions along the sensing fiber. Theoretical analysis indicates that the Haar\nwavelet transform tends to represent abrupt signals as prominent wavelet\ncoefficients, while its inverse transform process can effectively reconstruct\nsignals with step characteristics. This property is crucial in the denoising\nprocess of Raman distributed optical fiber sensing technology: through\ntargeted threshold processing, it can not only effectively suppress noise but\nalso maximize the retention of the signal structure that characterizes abrupt\ntemperature changes, thereby significantly alleviating the deterioration of the\nsystem's spatial resolution performance caused by traditional denoising\nmethods.\n[1] L. Xu, et al. RDTS noise reduction method based on\nICEEMDAN-FE-WSTD. IEEE Sens. J. 22(18): 17854-17863 (2022).\n[2] M. A. Soto, et al. Raman-based distributed temperature sensor with 1 m\nspatial resolution over 26 km SMF using low-repetition-rate cyclic pulse\ncoding. Opt. Lett. 36(13): 2557-2559 (2011).\n[3] X. Z. Sun, et al. Genetic-optimised aperiodic code for distributed optical\nfibre sensors. Nat. Commun. 11(1), 5774 (2020).\n[4] J. Park, et al. Raman-based distributed temperature sensor with simplex\ncoding and link optimization. IEEE Photonics Technol. Lett. 18(17):\n1879-1881 (2006).\n[5] J. B. Rosolem, et al. Raman DTS based on OTDR improved by using\ngain-controlled EDFA and pre-shaped simplex code. IEEE Sens. J. 17(11):\n3346-3353 (2017).\n[6] D. D. Chai, et al. Derived sequences decoding approach for long-range\ndistributed temperature sensors. IEEE Sens. J. 23(3): 2204-2210 (2022).\n\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Introduction, page 2, right column, paragraph 2,\nline 3, add “Algorithm denoising schemes aim to improve the SNR\nof the system by processing optical fiber scattering signals. For\nexample, M. Yu, et al. proposed a dynamic sampling-correction\nscheme achieving a sensing distance of 20.0 km [23]. H. S. Pradhan,\net al. proposed a Fourier wavelet regularised deconvolution scheme\nachieving a sensing distance of 30.0 km with a spatial resolution of\n3.0 m [24]. Essentially derived from mathematical optimization\ntheory, such schemes only denoise signals from the perspective of\nsignal processing without achieving breakthroughs in physical\nmechanisms. Furthermore, they have limitations including parameter\ndependence and difficulty in preserving the true characteristics of\nsignals [30].\nIn addition, as one of the current mainstream denoising\nmethods, convolutional neural networks (CNNs) scheme is a typical\ndata-driven approach. It optimizes model parameters using\nlarge-scale training datasets, with the goal of achieving effective\nprocessing of test data. For example, Z. Zhang, et al. proposed a\ndeep 1-D denoising convolutional neural network scheme, which\nrealized a sensing distance of 10 km with a spatial resolution of 3 m\n[26]. However, the performance of this method is significantly\nconstrained by the specificity of training data; when there is a\nnotable distribution difference between test signals and the training\nset, its effect on enhancing sensing performance will be limited.”\n2) In the (unmodified manuscript) section of Introduction, page 3,\nleft column, paragraph 2, line 3, delete“ In this work, an enhanced\nautocorrelation pulse coding (EAC-coding) scheme is proposed,\nwhich introduces Golay complementary sequences into Raman\ndistributed optical fiber sensing, and at the same time restores the\nautocorrelation which is destroyed by the transient effects of\nerbium-doped fiber amplifier (EDFA) by preprocessing the Raman\nbackscattered signals for analysis and waveform-reconstruction. The\nproposed scheme further incorporates Haar wavelet denoising\nalgorithm to enhance system performance. In the experiment, a\nRaman distributed optical fiber sensing with sensing distance of 70.0\nkm, spatial resolution of 1.58 m and temperature resolution of 5.39 ℃\nis achieved, which provides a new solution for the research of\nlong-distance Raman distributed optical fiber sensing.”\n3) In the section of Introduction, page 4, left column, paragraph 3,\nline 22, add “Currently, existing pulse coding techniques in Raman\ndistributed optical fiber sensing remain constrained by several\nprevalent bottlenecks: high hardware implementation complexity,\nexcessive computational overhead in encoding and decoding, limited\nnonlinear effect suppression capability, and inadequate resistance to\nsignal distortion coupled with poor stability during long-distance\ntransmission. Collectively, these factors constrain the system’s\napplication potential in high-performance scenarios—including low\nSNR environments and long-distance sensing applications.\nTo address the aforementioned issues, an Enhanced\nanti-distortion coding (EAC-coding) scheme is proposed in this\npaper. This scheme effectively overcomes the trade-off dilemma\namong SNR, sensing distance, and hardware cost in traditional\nmethods through a three-fold synergistic mechanism: compensating\nfor EDFA fluctuation via a preprocessing framework, suppressing\ntransmission losses through coding gain, and finely removing\nresidual noise using wavelet transform. While maintaining relatively\nlow complexity, the EAC-coding scheme significantly enhances\nthe anti-distortion capability and adaptability of the system, providing a\nnew solution for long-distance, high-performance Raman distributed\noptical fiber sensing. Experimental results demonstrate that at an\nultra-long distance of 70.0 km, the system achieves a spatial\nresolution of 1.58 m and a temperature resolution of 5.39 ℃, with\nthe number of effective sensing points reaching 44,303. To the best\nof our knowledge, this number of effective sensing points represents\nthe highest level in the field of Raman distributed optical fiber\nsensing. In addition, the preprocessing architecture within\nEAC-coding (autocorrelation characteristic analysis, waveform\nanalysis and reconstruction of Raman backscattered signals)\nsignificantly enhances the temporal fidelity and transmission\nstability of encoded sequences by dynamically compensating for\nEDFA transient gain fluctuation. This further improves the SNR and\ntemperature measurement accuracy performance, enabling the\ntemperature measurement accuracy to reach 0.91 ℃, verifying the\nengineering feasibility of the scheme.”\n4) In the (unmodified manuscript) section of Experimental results,\npage 10, right column, paragraph 2, line 29, delete “Raman\ndistributed optical fiber sensing has emerged as a pivotal technology\nfor continuous temperature monitoring in long-range infrastructure\nand environmental applications. However, its practical\nimplementation over distances exceeding 30 km has been\nfundamentally hindered by the inherently low signal-to-noise ratio\n(SNR) of Raman scattering signals, which creates a critical trade-off\nbetween sensing distance and spatial resolution. In this study, we\npresent a novel Raman distributed optical fiber sensing system\nutilizing the proposed EAC-coding scheme, which effectively\nsuppresses transient effects and significantly enhances the SNR of\nsystem while incorporating Haar wavelet. This system enables\nlong-distance Raman distributed temperature measurement with\nhigh spatial resolution, achieving precise temperature demodulation\nand accurate identification of FUT position and length. The\nexperimental results demonstrate that the proposed scheme achieves\na spatial resolution of 1.58 m, temperature resolution of 5.39 ℃, and\ntemperature measurement accuracy of 0.88 ℃ at the sensing\ndistance of 70.0 km, establishing a new approach for long-distance\nRaman distributed optical fiber sensing system. Future research will\nintegrate more advanced denoising techniques to extend the system's\nsensing distance while preserving its spatial resolution capabilities.”\n5) In the section of Experimental results, page 18, left column,\nparagraph 2, line 10, add “EAC-coding scheme proposed in this\npaper incorporates a novel preprocessing framework for\nautocorrelation characteristic analysis, waveform analysis and\nreconstruction of Raman backscattered signals. The preprocessing\narchitecture for autocorrelation characteristic analysis, waveform\nanalysis and reconstruction in this scheme can effectively suppress\nthe transient effects introduced by EDFA, thereby significantly\nimproving the amplitude fidelity and temporal stability of the\nencoded pulse sequence. This innovative active reconstruction\nmechanism in the signal domain, which is based on analyzing the\nwaveforms of Raman backscattered signals via forward/inverse\nFourier transforms, directly eliminates the phenomenon of detection\npulse distortion existing in traditional demodulation schemes. The\nscope of action of the EAC-coding scheme encompasses two key\naspects: specifically, one is addressing the fundamental limitation of\ndetection signal distortion through physical-layer waveform\nreconstruction, and the other is performing correlation operations\nbetween the proposed coding sequence and the reconstructed Raman\nsignal to restore the ideal cross-correlation characteristics of Golay\nsequences, and achieve a theoretical gain value, thereby breaking\nthrough the SNR-distance trade-off limit. It achieves the\ncoordinated optimization of “waveform correction, correlation characteristic\nrestoration, signal intensity enhancement”, laying a physical layer\nfoundation for long-distance sensing.\nFurthermore, the proposed EAC-coding scheme features a\nsynergistically enhanced two-stage noise suppression mechanism,\ndemonstrating innovations in multi-level joint denoising.\nFirst, EAC-coding scheme enhances the SNR of sensing signals\nthrough its inherent coding gain. Based on the cross-correlation\ncharacteristics of its sequence design, this coding scheme provides a\nsignificant inherent gain, which compensates for signal attenuation\ncaused by long-distance transmission and effectively improves the\nsystem's baseline SNR. Furthermore, this mechanism not only\nsignificantly boosts optical power but also leverages the irrelevance\nbetween the decoding algorithm and incoherent noise to achieve\npreliminary suppression of transmission link losses at the\nencoding-decoding level.\nSecond, aiming at the residual noise with specific\ntime-frequency domain distribution characteristics in the decoded\nsignal, this scheme further introduces Haar wavelet transform for\nadaptive noise filtering. The multi-resolution analysis capability of\nthe Haar wavelet enables accurate capture of the local\ntime-frequency features of noise. By performing sparse\nrepresentation of the signal at different scales (corresponding to\ndifferent frequency bands) and time-domain positions, it achieves\neffective separation between useful signals and non-stationary noise\ncomponents. While preserving the key details of the distributed\ntemperature signal, this method efficiently eliminates residual noise,\nsignificantly enhancing the clarity of the signal in the\ntime-frequency domain and the overall measurement accuracy of the\nsystem.\nThis three-fold synergistic mechanism, consisting of the\npreprocessing framework compensating for EDFA fluctuation,\ncoding gain suppressing transmission losses, and wavelet transform\nfinely removing residual noise, systematically breaks through the\nbottlenecks of traditional schemes in terms of SNR and sensing\ndistance, providing a novel decoding framework for long-distance\nand high-precision Raman distributed optical fiber sensing.”\n6) In the section of Experimental results, page 13, left column,\nparagraph 2, line 18, add “In this study, a denoising algorithm\nbased on the Haar wavelet is adopted to process distributed\ntemperature sensing signals with abrupt change characteristics. The\ninherent step-like form of the Haar wavelet basis function endows it\nwith excellent feature extraction capability for singular points in the\nsignal, especially for the abrupt temperature field change regions\nalong the sensing fiber.”\n7) In the section of Introduction, page 3, left column, paragraph 3,\nline 27, add “The main limitation of this scheme lies in the linear\ngrowth of data acquisition volume and computational complexity\nwith code length, which restricts its practical efficiency in\napplications requiring long code lengths and high-speed sensing.”\n8) In the section of Introduction, page 3, right column, paragraph 1,\nline 9, add “However, higher pulse energy also makes it more likely\nto induce fiber nonlinear effects, and when approaching the\nstimulated scattering threshold, it restricts the system’s sensing\ndistance and SNR performance.”\n9) In the section of Introduction, page 3, right column, paragraph 2,\nline 25, add “Although this scheme effectively suppresses the\ntransient response of the EDFA at the hardware level, its hardware\nstructure is more complex, leading to a significant increase in\nimplementation cost.”\n10) In the section of Introduction, page 4, left column, paragraph 1,\nline 3, add “The core challenge of this scheme lies in its high\ndependence on optimization algorithms to search for the optimal\ncode, which typically requires substantial computational resources\nand iterative testing.”\n11) In the section of Introduction, page 4, left column, paragraph 2,\nline 17, add “However, this scheme’s decoding process imposes a\nheavy computational burden, and the core algorithm involves\nhigh-complexity matrix operations, making it difficult to meet\nreal-time requirements.”\n\n2. As the core innovation of this work, the uniqueness of Golay-encode\nautocorrelation processing is insufficiently explained. How does it compare\nquantitatively to other well established coding methods such as Simplex coding and\ngenetic-optimized aperiodic coding? For example, maybe the discussion can be made\nfrom the perspective of coding gain and measurement time. After all, the physical\nreason that the record-breaking performance can be achieved should be explicitly\npointed out.\n\nReply: We sincerely appreciate the reviewers' professional and valuable\nsuggestions. We believe that the innovation of this manuscript has been\nsignificantly enhanced after revisions based on your comments. In\naccordance with the reviewers' professional advice, we have compared our\nproposed scheme with other coding methods such as simplex coding and\nGenetic-optimised aperiodic coding in terms of coding gain, measurement\ntime, and system complexity. The specific revisions are as follows.\nIn terms of coding gain, the EAC-coding scheme proposed in this\nmanuscript exhibits significant advantages in SNR improvement. The core of\nthis scheme lies in the analysis and accurate reconstruction of the waveform\nof Raman backscattered signals, which effectively compensates for the\ndistortion of detection signals caused by transient effects. This mechanism\nenables EAC-coding to overcome the performance bottleneck of traditional\nderived sequences coding schemes induced by signal distortion, thereby\nachieving a coding gain that is closer to the theoretical limit. Specifically,\nexisting derived sequences coding schemes construct coding sequences based\non Golay complementary sequences and perform correlation decoding using\ntheir derived sequences. The upper limit of their theoretical coding gain is\n√L/2 (where L denotes the length of the coding sequence) [1]. However, due\nto the unavoidable distortion (especially transient distortion) in actual\ndetection signals, the results of their correlation operations are degraded,\nleading to a significant gap between the actual coding gain obtained and this\ntheoretical value. In contrast, the EAC-coding scheme, through the\nautocorrelation characteristic analysis, waveform analysis and reconstruction\nof Raman backscattered signals, significantly suppresses the impact of\ntransient distortion on the detected waveform, allowing its coding gain to\napproach the theoretical upper limit of √L/2. Benefiting from this, the\nproposed system ultimately achieves the capability of temperature sensing in\na long-distance Raman distributed optical fiber sensing system with a sensing\ndistance of 70.0 km.\nIn terms of measurement time, the core advantage of the EAC-coding\nscheme stems from its extremely low decoding computational complexity.\nThis scheme achieves signal reconstruction solely through Fourier transform,\nwhich significantly reduces the computational cost and time delay of\nreal-time data processing, thereby effectively improving the overall response\nspeed of the system. Details are as follows: For a Simplex code with a code\nlength of L, it is necessary to inject L groups of detection signals into the\noptical fiber and collect L groups of Raman backscattered signals; its\ntheoretical minimum acquisition time is given by T =L×t (where t\nSimplex\ndenotes the acquisition time of a single group of Raman backscattered\ncurves) [2]. Although Genetic-optimised aperiodic coding only requires\ninjecting one group of detection signals into the optical fiber, it necessitates\nadditional time to design coding sequences based on the distributed genetic\nalgorithm.\nDerived Sequences coding requires injecting 4 groups of detection signals\ninto the optical fiber (theoretical acquisition time of 4t), and during the\ndecoding stage, it involves complex procedures such as extracting the\nattenuation envelope, establishing a compensation model, and solving the\ncompensation envelope via matrix operations—all of which increase the time\ncost of the decoding process. The EAC-coding scheme proposed in this\nmanuscript performs coding based on Golay complementary sequences, with\na theoretical acquisition time of 4t, and only needs Fourier transform to\ncomplete the analysis and reconstruction of the Raman backscattered signal\nwaveform. This significant efficiency improvement at the algorithm level\ngreatly reduces the delay in real-time data processing, effectively enhances\nthe system response speed, and provides crucial real-time performance\nguarantees for the final realization of a 70.0 km long-distance Raman\ndistributed optical fiber sensing system.\nIn terms of system complexity, the core innovation of the\nEAC-coding scheme lies in achieving a high degree of simplification in the\ndecoding process through algorithm optimization, while keeping the hardware\narchitecture unchanged. This scheme only needs to perform efficient Fourier\ntransform operations to complete signal reconstruction, which significantly\nreduces the algorithmic complexity and computational burden of real-time\ndata processing. The specific reasons are as follows. Simplex coding scheme\nrequires the injection of L groups of detection signals, resulting in a long\nacquisition time and a large volume of raw data. This not only imposes high\nrequirements on hardware performance (such as data acquisition rate and\nstorage capacity) and long-term stability, but also the large-scale data\nprocessing involved in its decoding process significantly increases the\ncomputational complexity. Genetic-optimised aperiodic coding scheme\ngreatly shortens the acquisition time without increasing hardware costs.\nHowever, due to its unique design, it is necessary to design coding sequences\nbased on a distributed genetic algorithm and conduct extensive tests to find\nthe optimal coding sequence. Derived sequences coding scheme also does\nnot require additional hardware overhead. However, this scheme introduces\nhigh computational complexity in the decoding stage, as it relies on\ncomputationally expensive matrix operations to generate and process derived\nsequences.\n[1] D. D. Chai, et al. Derived sequences decoding approach for long-range\ndistributed temperature sensors. IEEE Sens. J. 23(3): 2204-2210 (2022).\n[2] J. Park, et al. Raman-based distributed temperature sensor with simplex\ncoding and link optimization. IEEE Photonics Technol. Lett. 18(17):\n1879-1881 (2006).\n\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Discussion, page 19, right column, paragraph 4,\nline 7, add “Currently, the pulse coding techniques applied in\nRaman distributed optical fiber sensing system mainly include the\nfollowing: Simplex coding scheme, Pre-Shaped Simplex coding\nscheme, Low-repetition-rate cyclic pulse coding scheme,\nGenetic-optimised aperiodic coding scheme, and Derived Sequences\ncoding scheme. Their key performance indicators are presented in\nTable 2.\nTable 2. Sensing performance of various coding schemes.\nWe have compared our proposed scheme with other coding\nmethods such as simplex coding and Genetic-optimised aperiodic\ncoding in terms of coding gain, measurement time, and system\ncomplexity. The specific revisions are as follows.\nIn terms of coding gain, the EAC-coding scheme proposed in\nthis paper exhibits significant advantages in SNR improvement. The\ncore of this scheme lies in the analysis and accurate reconstruction\nof the waveform of Raman backscattered signals, which effectively\ncompensates for the detection signals distortion caused by the\ntransient effects of the system. This mechanism enables EAC-coding\nto overcome the performance bottleneck of traditional derived\nsequences coding schemes induced by signals distortion, achieving a\ncoding gain closer to the theoretical limit. Specifically, existing\nderived sequence coding scheme construct coding sequences based\non Golay complementary sequences and perform correlation\ndecoding using their derived sequences. The upper limit of their\ntheoretical coding gain is √L/2 (where L denotes the length of the\ncoding sequence). However, due to the unavoidable distortion\n(especially transient distortion) in actual detection signals, the\nresults of their correlation operations deteriorate, leading to a\nsignificant gap between the actually achieved coding gain and this\ntheoretical value. In contrast, the EAC-coding scheme, through the\naforementioned signals analysis and reconstruction mechanism,\nsignificantly suppresses the impact of transient distortion on the\ndetection signals waveform, thereby enabling its coding gain to\napproach the theoretical upper limit of √L/2. Benefiting from this,\nthe proposed system ultimately achieves temperature sensing\ncapability in a long-distance Raman distributed optical fiber sensing\nsystem with a sensing distance of 70.0 km.\nIn terms of measurement time, the core advantage of the\nEAC-coding scheme stems from its extremely low decoding\ncomputational complexity. This scheme achieves signals\nreconstruction solely through Fourier transform, which significantly\nreduces the computational cost and time delay of real-time data\nprocessing, thereby effectively improving the overall response speed\nof the system. Specifically, for a Simplex code with length L, it is\nnecessary to inject L groups of detection signals into the optical fiber\nand collect L groups of Raman backscattered signals, with its\ntheoretical minimum acquisition time being T =L×t (where t\nSimplex\ndenotes the acquisition time of one group of Raman backscattered\ncurves). Although the Genetic-optimised aperiodic coding scheme\nonly requires injecting one group of detection signals into the optical\nfiber, it needs additional time to design the coding sequence based\non the distributed genetic algorithm. The Derived sequences coding\nscheme requires injecting 4 groups of detection signals into the\noptical fiber, with a theoretical acquisition time of 4t. However, in\nthe decoding stage, it involves complex steps such as extracting the\nattenuation envelope, establishing a compensation model, and\nsolving the compensation envelope via matrix operations, which\nincreases the time cost of the decoding process. The EAC-coding\nscheme proposed in this paper performs encoding based on Golay\ncomplementary sequences, with a theoretical acquisition time of 4t,\nand only needs Fourier transform to complete the analysis and\nreconstruction of the Raman backscattered signals waveform. This\nsignificant efficiency improvement at the algorithm level greatly\nreduces the real-time data processing delay and effectively enhances\nthe system response speed, providing crucial real-time guarantee for\nthe final realization of temperature sensing in a 70.0 km\nlong-distance Raman distributed optical fiber sensing system.\nIn terms of system complexity, the core innovation of the\nEAC-coding scheme lies in achieving a high degree of\nsimplification in the decoding process through algorithm\noptimization, while keeping the hardware architecture unchanged.\nThis scheme only needs to perform efficient Fourier transform\noperations to complete signal reconstruction, which significantly\nreduces the algorithmic complexity and computational burden of\nreal-time data processing. The specific reasons are as follows.\nSimplex coding scheme requires the injection of L groups of\ndetection signals, resulting in a long acquisition time and a large\nvolume of raw data. This not only imposes high requirements on\nhardware performance (such as data acquisition rate and storage\ncapacity) and long-term stability, but also the large-scale data\nprocessing involved in its decoding process significantly increases\nthe computational complexity. Genetic-optimised aperiodic coding\nscheme greatly shortens the acquisition time without increasing\nhardware costs. However, due to its unique design, it is necessary to\ndesign coding sequences based on a distributed genetic algorithm\nand conduct extensive tests to find the optimal coding sequence.\nDerived sequences coding scheme also does not require additional\nhardware overhead. However, this scheme introduces high\ncomputational complexity in the decoding stage, as it relies on\ncomputationally expensive matrix operations to generate and\nprocess derived sequences.\nEAC-coding scheme proposed in this paper incorporates a\nnovel preprocessing framework for autocorrelation characteristic\nanalysis, waveform analysis and reconstruction of Raman\nbackscattered signals. This framework significantly improves the\nfidelity and transmission stability of the encoded pulse sequence by\ndynamically compensating for the transient gain fluctuation of\nEDFA. This technology leverages the inherent gain of EAC-coding\npulse coding to effectively offset fiber scattering attenuation during\n70.0 km long-distance transmission, achieving a significant\nimprovement in the baseline SNR. On this basis, a two-stage noise\nsuppression method is further constructed. The first-stage processing\ninvolves compensating for signal attenuation using the theoretical\ncoding gain of EAC-coding. For the second-stage processing, a Haar\nwavelet denoising algorithm is adopted. Its step-matching\ncharacteristic enables accurate extraction of the abrupt temperature\nchange features of the sensing fiber and adaptive filtering of the\nresidual time/frequency domain coupled noise in the decoded signal.\nThis three-fold synergistic mechanism, consisting of the\npreprocessing framework compensating for EDFA fluctuation,\ncoding gain suppressing transmission losses, and wavelet transform\nfinely removing residual noise, breaks through the theoretical\ntrade-off bottleneck between SNR and sensing distance in traditional\nschemes. Experiment results indicate that, at an ultra-long distance\nof 70.0 km, this scheme can achieve a spatial resolution of 1.58 m, a\ntemperature resolution of 5.39 °C, and an effective number of\nsensing points reaching 44,303, verifying the engineering feasibility\nof the scheme. To the best of our knowledge, the number of\neffective sensing points achieved by this scheme ranks the highest in\nthe field of Raman distributed optical fiber sensing systems.”\n\n3. To let the reader to better evaluate the performance in this work, a quantitative and\nfair comparison with the state of the art should be made. If possible, a figure of merit\nshould be given that normalizes the measurement time, considering that the\nperformance in this work is obtained over one hour.\n\nReply: Thank you for your valuable suggestions, which are of great\nhelp in enhancing the innovation of this manuscript and guiding the research\nwork to be carried out in the future. Based on the reviewer's professional\nsuggestions, we have quantitatively analyzed the measurement time in the\ndiscussion section. Furthermore, we have compared and elaborated on the\nkey performance indicators of our proposed scheme with those of existing\ncoding techniques. The revised content is as follows.\nCurrently, in the field of Raman distributed optical fiber sensing, a\nperformance comparison between conventional coding schemes and the\nproposed EAC-coding scheme is presented in Table 3.\nSimplex coding scheme, as a linear coding technique based on\nHadamard matrix transformation, has its code length (in L bits) determining\nthe number of detection signals required (L groups). By leveraging the\nSimplex coding and link optimization technology, a spatial resolution of 17.0\nm, a temperature resolution of 3.0 °C, and an effective number of sensing\npoints of 2176 have been achieved at a sensing distance of 37.0 km [1].\nLow-repetition-rate cyclic pulse coding scheme generates Simplex\ncoding-based cyclic coding sequences using an acousto-optic modulator\n(AOM), enabling pulses to be injected into the optical fiber periodically at a\nlow repetition rate. The combination of low-repetition-rate cyclic pulse\ncoding and a high-power fiber laser achieves a spatial resolution of 1.0 m, a\ntemperature resolution of 3.0 °C, an effective number of sensing points of\n26,000, and a measurement time of 30 s at a sensing distance of 26.0 km [2].\nPre-Shaped Simplex Coding scheme is based on simplex coding\ntechnology and adopts a linearly increasing profile to adjust pulse amplitude,\ncompensating for the amplitude variation caused by EDFA to suppress the\ntransient effect of EDFA and improve system performance. Based on\npre-shaped Simplex coding and a gain-controlled EDFA, a spatial resolution\nof 10.0 m, a temperature resolution of 8.4 °C, and an effective number of\nsensing points of 6,200 have been achieved at a sensing distance of 62.0 km\n[3].\nGenetic-optimised aperiodic coding scheme utilizes a distributed\ngenetic algorithm (DGA) to generate a single-sequence aperiodic code\n(GO-code), which is then converted into an optical pulse sequence and\ninjected into the optical fiber. This scheme achieved a spatial resolution of\n1.0 m, a temperature resolution of 3.9 °C, an effective number of sensing\npoints of 39,000, and a measurement time of 13.6 min at a sensing distance\nof 39.0 km [4].\nDerived Sequences coding scheme addresses the transient effect of\nEDFA through a derived sequence decoding method, thereby enhancing the\nperformance of long-distance sensing. Based on the Derived Sequences\ncoding scheme, a spatial resolution of 5.0 m, a temperature resolution of 2.5 °C, and an effective number of sensing points of 8,800 have been\nachieved at a sensing distance of 44.0 km [5].\nEAC-coding scheme proposed in this manuscript incorporates a novel\npreprocessing framework for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered signals. This\nframework significantly improves the fidelity and transmission stability of\nthe encoded pulse sequence by dynamically compensating for the transient\ngain fluctuation of EDFA. This technology leverages the inherent gain of\nEAC-coding pulse coding to effectively offset fiber scattering attenuation\nduring 70.0 km long-distance transmission, achieving a significant\nimprovement in the baseline SNR. On this basis, a two-stage noise\nsuppression method is further constructed. The first-stage processing\ninvolves compensating for signal attenuation using the theoretical coding\ngain of EAC-coding. For the second-stage processing, a Haar wavelet\ndenoising algorithm is adopted. Its step-matching characteristic enables\naccurate extraction of the abrupt temperature change features of the sensing\nfiber and adaptive filtering of the residual time/frequency domain coupled\nnoise in the decoded signal. This three-fold synergistic mechanism,\nconsisting of the preprocessing framework compensating for EDFA\nfluctuation, coding gain suppressing transmission losses, and wavelet\ntransform finely removing residual noise, breaks through the theoretical\ntrade-off bottleneck between SNR and sensing distance in traditional\nschemes. Experiment results indicate that, at an ultra-long distance of 70.0\nkm, this scheme can achieve a spatial resolution of 1.58 m, a temperature\nresolution of 5.39 °C, and an effective number of sensing points reaching\n44,303, verifying the engineering feasibility of the scheme.\nFurthermore, the measurement time of the scheme proposed in this\nmanuscript is mainly limited by the massive data volume (with the effective\nnumber of sensing points reaching 44,303) and the hardware accumulation\nprocessing time of the acquisition card, which are caused by its long sensing\ndistance and high spatial resolution—rather than the complexity of its\nprocessing architecture. The current measurement time (252 min) is\nconstrained by"}, "author_response": "Response to the reviewers’ comments\nThank you very much for your consideration of our manuscript entitled “Overcoming\nthe Longstanding Challenge of Long-Range Raman Distributed Optical Fiber Sensing\nThrough Enhanced Anti-distortion Coding and Waveform Reconstruction” by Fan\nZhang, Jian Li, Lulei Li, Kangyi Cao and Mingjiang Zhang.\nWe would like to thank the reviewers for their efforts to review our manuscript and\ntheir appreciation of the novelty and quality of our work. The constructive\nsuggestions from the reviewers have been thoroughly considered and implemented in\nthe revised manuscript, which now has been significantly improved.\nIn the next several pages, the changes made to the manuscript are detailed to fully\naddress the concerns raised according to each of the reviewers’ comments. We hope\nthe manuscript is now appropriate for publication in Nature Communications.\nIn addition, we would like to declare:\n(1) All authors agree with the submission.\n(2) The work has not been published or submitted for publication elsewhere, either\ncompletely or in part, or in another form or language.\n(3) No materials are reproduced from another source.\n(4) The authors declare no conflicts of interest.\nWe look forward to hearing from you!\nWith best regards,\nJian Li, Mingjiang Zhang\nAll the reviewers’ suggestions have been considered. The following are the changes\nmade in the manuscript to fully address the reviewers’ concerns:\nBlue: Original comments from the reviewer.\nBlack: Our response including action taken.\nResponds to the reviewers’ comments:\nReviewer 1 (Comments to the Author):\nRecommendations for the Author(s):\nThe authors present a novel manuscript discussing a long-range Raman distributed\noptical fiber sensing scheme through Golay-encoded autocorrelation and waveform\nreconstruction technology. The practical implementation of Raman-based distributed\noptical fiber sensing has been fundamentally constrained by the inherent low\nsignal-to-noise ratio, particularly for operational ranges exceeding 30 km. The authors\npropose a ground breaking paradigm integrating Golay-encoded autocorrelation\nprocessing with advanced Raman scattering waveform reconstruction to transcend\nthis physical limitation. And the newly developed preprocessing framework\nsimultaneously optimizes complementary sequence correlation and effectively\nmitigates disturbances of transient effects. The experimental results demonstrate a\nsensing performance of 70 km operational range with1.58m spatial resolution, while\nmaintaining0.88℃ measurement accuracy. To my knowledge, this represents the first\nwork in achieving such a long sensing distance with 1meter-level spatial resolution.\nThe manuscript can be accepted if the following comments are addressed:\nReply: Thank you very much for your positive comments on the content\nof our research and constructive suggestions on the manuscript. Those\ncomments are all valuable and very helpful for revising and improving our\nmanuscript, as well as the important guiding significance to our research. We\nhave studied the comments carefully and have made corrections which we\nhope meet with approval.\n1. In Raman distributed temperature sensing systems, spatial resolution is intrinsically\ndetermined by the probing pulse duration, as the pulse width directly defines the\nminimum spatial discrimination through time-of-flight measurements. The paper\nexplicitly states that the pulse width of a single code element is set to 10 ns and\nsingle-mode fiber is employed to avoid spatial resolution degradation due to\nintermodal dispersion. However, the experimental results show that the achieved\nspatial resolution failed to reach the theoretical spatial resolution of 1m. What is the\nreason for the different between theoretical prediction and experimental outcome?\nReply: Thank you very much for your professional comments, and we\nfully agree with the viewpoints. The reason for the slight discrepancy\nbetween the theoretical spatial resolution and the experimental spatial\nresolution in this manuscript lies in the fact that the Haar and db10\n(Daubechies wavelet 10) wavelet denoising methods used in the experiment\nwill filter out the edge information of the temperature envelope in the sensing\nfiber region, which leads to the error between the experimental spatial\nresolution and the theoretical spatial resolution of the system. The specific\nreasons are as follows.\nIn this manuscript, the pulse width of a single code element is set to 10\nns, corresponding to a theoretical spatial resolution of 1.0 m. Furthermore,\nsingle-mode fiber is employed to avoid the degradation of spatial resolution\ncaused by intermodal dispersion in the sensing fiber. However, the intensity\nof Raman scattering signals excited in single-mode fiber is relatively low.\nTherefore, in the experiment, to further improve the SNR of the sensing\nsignals, Haar wavelet denoising processing is applied to the Raman\nanti-Stokes scattering signals after the decoding process. It is suitable for\nprocessing low-complexity signals with mutation characteristics, thus making\nit well-suited for handling fiber optic Raman scattering signals. Meanwhile,\nin this manuscript, after temperature demodulation, the db10 wavelet method\nis synchronously applied to the distributed temperature demodulation curve\nto further improve the SNR of the sensing signal. However, this denoising\nmethod will filter out the edge information of the temperature envelope in the\nsensing fiber region, resulting in a final experimentally measured spatial\nresolution of 1.58 m, which differs from the theoretical spatial resolution of\n1.0 m.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental results, page 17, right column,\nparagraph 2, line 11, add “In the proposed scheme, the pulse width\nof a single code element is set to 10 ns, corresponding to a\ntheoretical spatial resolution of 1.0 m. Furthermore, single-mode\nfiber is employed to avoid the degradation of spatial resolution\ncaused by intermodal dispersion in the sensing fiber. However, the\nintensity of Raman scattering signals excited in single-mode fiber is\nrelatively low. Therefore, in the experiment, to further improve the\nSNR of the sensing signals, Haar wavelet denoising processing is\napplied to the Raman anti-Stokes scattering signals after the\ndecoding process. It is suitable for processing low-complexity\nsignals with mutation characteristics, thus making it well-suited for\nhandling fiber optic Raman scattering signals. Meanwhile, in this\npaper, after temperature demodulation, the db10 wavelet method is\nsynchronously applied to the distributed temperature demodulation\ncurve to further improve the SNR of the sensing signal. However,\nthis denoising method will filter out the edge information of the\ntemperature envelope in the sensing fiber region, resulting in a final\nexperimentally measured spatial resolution of 1.58 m, which differs\nfrom the theoretical spatial resolution of 1.0 m.”\n2. The method mentioned in this paper only explores the effect of the transient effect\non anti-Stokes light in analyzing the transient effect. And only the anti-Stokes light is\nused in the temperature demodulation process, discarding the use of Stokes signals.\nHow does this differ from the traditional dual-channel demodulation scheme that\nrelies on both anti-Stokes and Stokes signals, and what are its significant advantages?\nReply: We sincerely appreciate the reviewer’s professional comments.\nIn the experimental process of this scheme, only the Raman anti-Stokes\nscattering signals were analyzed and processed, and the subsequent\ntemperature demodulation was also performed solely based on the Raman\nanti-Stokes scattering signals. Compared with the dual-path demodulation\nscheme (where Raman Stokes scattering light is used to demodulate Raman\nanti-Stokes scattering signals), this scheme has the following two specific\nadvantages.\n(1) The Raman anti-Stokes scattering signal based on single-path\ndemodulation exhibits higher sensitivity to the temperature distribution\nalong the sensing fiber. Moreover, due to its simpler signal processing link\nand the elimination of the need for additional light splitting or switching\nmechanisms, the single-path demodulation scheme is more easily integrated\nwith the Golay code modulation technology proposed in this manuscript at\nthe hardware implementation level. Therefore, the characteristics of\nsingle-path demodulation, such as its low-complexity signal link, high\nhardware compatibility, and absence of multi-path signal conflicts, are highly\ncompatible with the requirements of pulse coding for signal integrity and\nhardware integration.\n(2) The single-path demodulation scheme can enhance the system's\nmeasurement rate and reduce system costs. In the dual-path demodulation\nscheme, both the calibration process and the measurement process require\nindependent acquisition of two channels of scattering signals, resulting in a\ndoubling of the original data volume. This not only approximately doubles\nthe overall measurement cycle of the system but also imposes higher\nrequirements on the storage depth of the data acquisition system, thereby\nincreasing the system cost.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental setup, page 9, right column,\nparagraph 2, line 4, add “In the experimental process of this\nscheme, only the Raman anti-Stokes scattering signals were\nanalyzed and processed, and the subsequent temperature\ndemodulation was also performed solely based on the Raman\nanti-Stokes scattering signals. Compared with the dual-path\ndemodulation scheme (where Raman Stokes scattering light is used\nto demodulate Raman anti-Stokes scattering signals), this scheme\nhas the following two specific advantages. The Raman anti-Stokes\nscattering signal based on single-path demodulation exhibits higher\nsensitivity to the temperature distribution along the sensing fiber;\nThe single-path demodulation scheme can enhance the system's\nmeasurement rate and reduce system costs.”\n3. The experimental setup section lacks detailed descriptions of the specific types and\nparameters for each device, which may hinder readers from reproducing the\nexperiment. It is advisable to supplement the detailed specifications of the optical\ncomponents used, including their models, manufacturers, and key optical parameters.\nReply: We sincerely appreciate the reviewer’s professional suggestions.\nIn the revised manuscript, we have supplemented the model numbers,\nmanufacturers, and key optical parameters of the equipment used in the\nexperiments. The detailed supplementary information is as follows.\n① Laser (KEYANG PHOTONICS; DFB Continuous laser; Center\nWavelength:1550 nm)\n② SOA (OPEAK; OAM-SOA-PL-15-15-S; Operating Wavelength:\n1520-1570 nm)\n③ DDPG (CIQTEK; ASG8100; Maximum Coding bit: 99 bit)\n④ EDFA (OPEAK; EDFA-C-PL-MB-100-S; Operating Wavelength:\n1550 nm)\n⑥ WDM (OPEAK; WDM-1*3-1550; Isolation: ≥60 dB)\n⑦ APD (KEYANG PHOTONICS; KY-DTS-200M; Bandwidth:200\nMHz)\n⑧ DAC (CIQTEK; DAQ2100; Sampling Rate: 1 GSa/s)\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental setup, page 8, right column,\nparagraph 2, line 5, add “The equipment used in the experiment,\nalong with their corresponding model numbers, manufacturers, and\nkey optical parameters, are listed as follows: Laser (KEYANG\nPHOTONICS; DFB Continuous laser; Center Wavelength:1550\nnm);SOA (OPEAK; OAM-SOA-PL-15-15-S; Operating\nWavelength: 1520-1570 nm); DDPG (CIQTEK; ASG8100;\nMaximum Coding bit: 99 bit); EDFA (OPEAK;\nEDFA-C-PL-MB-100-S; Operating Wavelength: 1550 nm); WDM\n(OPEAK; WDM-1*3-1550; Isolation: ≥60 dB); APD (KEYANG\nPHOTONICS; KY-DTS-200M; Bandwidth:200 MHz); DAC\n(CIQTEK; DAQ2100; Sampling Rate: 1 GSa/s). And all\nexperimental equipment used in this experiment are conventional\ncommercial products available on the market.”\n4. In this paper, the Raman backscattered signals are analyzed by calculating the SNR\nin Fig.4, whereas only peak-to-peak values are compared in the wavelet denoising\nresults presented in Fig.5. It is recommended to include a SNR analysis to ensure\nconsistency in evaluation metrics across different experimental analyses.\nReply: Thank you very much for your professional comments, and we\nfully agree with the viewpoints. In Fig. 1, we have added an experimental\nanalysis and comparison of the changes in SNR of Raman scattering signals\nbefore and after wavelet denoising. The experimental results are as follows.\nAs shown in Fig. 1(c1) and 1(c2), the Haar wavelet function\nsignificantly improves the SNR for both the EAC-coding scheme proposed in this manuscript and the traditional single-pulse demodulation scheme.\nExperimental results indicate that after Haar wavelet denoising, the SNR of\nthe EAC-coding scheme and the traditional single-pulse demodulation\nscheme is increased by 7.63 dB and 2.92 dB, respectively. It is worth noting\nthat a relatively significant difference emerges between the two\ndemodulation schemes at the end of the sensing fiber. For single-pulse\nscheme, the effective Raman scattering signal is basically submerged by\nsystem noise beyond 42.0 km. After incorporating the Haar wavelet function,\nalthough the noise level is reduced, the signal is still submerged by noise\nbeyond 56.0 km. Therefore, the improvement in SNR at the end of the\nsensing fiber is relatively limited for the single-pulse scheme. This also\nconfirms that the wavelet denoising algorithm has a limited capability to\nimprove SNR in long-distance distributed optical fiber sensing demodulation\nschemes. Hence, we combine the EAC-coding scheme with Haar wavelet\ndenoising. Only by avoiding the effective Raman scattering signal being\nsubmerged by system noise as much as possible can the wavelet denoising\nalgorithm maximize the SNR of the sensing signal.\nFig. 1 (c1) SNR of Raman backscattered signals based on conventional single-pulse\nscheme at the end of sensing fiber. (c2) SNR of Raman backscattered signals based on\nEAC-coding scheme at the end of sensing fiber.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental results, page 12, right column,\nchange “Fig. 5” to “Fig. 5”\nFig. 5. Intensity of Raman backscattered signals based on EAC-coding\nscheme and conventional single-pulse. (a) Intensity of Raman backscattered\nsignals based on EAC-coding scheme and conventional single-pulse with and\nwithout Haar wavelet. (b1) Intensity of Raman backscattered signals based on\nconventional single-pulse at the end of sensing fiber. (b2) Intensity of Raman\nbackscattered signals based on EAC-coding scheme at the end of sensing fiber.\n(c1) SNR of Raman backscattered signals based on conventional single-pulse\nscheme at the end of sensing fiber. (c2) SNR of Raman backscattered signals\nbased on EAC-coding scheme at the end of sensing fiber.\n2) In the section of Experimental results, page 13, right column,\nparagraph 2, line 11, add “As shown in Fig. 5(c1) and 5(c2), the\nHaar wavelet function significantly improves the SNR for both the\nEAC-coding scheme proposed in this paper and the traditional\nsingle-pulse demodulation scheme. Experimental results indicate\nthat after Haar wavelet denoising, the SNR of the EAC-coding\nscheme and the traditional single-pulse demodulation scheme is\nincreased by 7.63 dB and 2.92 dB, respectively. It is worth noting\nthat a relatively significant difference emerges between the two\ndemodulation schemes at the end of the sensing fiber. For\nsingle-pulse scheme, the effective Raman scattering signal is\nbasically submerged by system noise beyond 42.0 km. After\nincorporating the Haar wavelet function, although the noise level is\nreduced, the signal is still submerged by noise beyond 56.0 km.\nTherefore, the improvement in SNR at the end of the sensing fiber is\nrelatively limited for the single-pulse scheme. This also confirms\nthat the wavelet denoising algorithm has a limited capability to\nimprove SNR in long-distance distributed optical fiber sensing\ndemodulation schemes. Hence, we combine the EAC-coding scheme\nwith Haar wavelet denoising. Only by avoiding the effective Raman\nscattering signal being submerged by system noise as much as\npossible can the wavelet denoising algorithm maximize the SNR of the sensing\nsignal.”\n5. This paper only compares the EAC-coding scheme with the traditional single pulse\nscheme in the experiment, which hinders the demonstration of its superiority. It is\nrecommended to include a table in the discussion section detailing the\nperformance metrics and comparative advantages/disadvantages of various mainstream techniques,\nthereby highlighting the superiority of this study.\nReply: We would like to express our sincere gratitude to the reviewer\nfor professional suggestions. In response to these valuable comments, we\nhave added a new table in the Discussion section, which provides a detailed\ncomparison of the performance metrics, advantages, and disadvantages of\nvarious current pulse coding techniques, as shown in Table 1. The modified\nand newly added contents are as follows.\nPulse coding schemes have demonstrated significant advantages in\nlong-distance Raman distributed optical fiber sensing system. On one hand,\nby encoding the detection optical pulses, this technology can significantly\nincrease the optical power injected into the sensing fiber while avoiding fiber\nnonlinear effects, thereby enhancing the intensity of effective sensing signals\nat the level of signal generation mechanism. On the other hand, at the data\nprocessing level, it leverages the separability between coded signals and\nuncoded noise to effectively suppress noise and improve the SNR of system.\nCurrently, pulse coding scheme applied in Raman distributed optical\nfiber sensing system are primarily classified into six categories, which\nspecifically include the Simplex coding scheme, Pre-Shaped Simplex Coding\nscheme, low-repetition-rate cyclic pulse coding scheme, Genetic-optimised\naperiodic coding scheme, Derived Sequences coding scheme, and\nEAC-coding scheme.\nSimplex coding scheme, as a linear coding technique based on\nHadamard matrix transformation, has its code length (in L bits) determining\nthe number of detection signals required (L groups). For instance, in 2006, J.\nPark, et al. achieved a spatial resolution of 17.0 m, a temperature\nresolution of 3.0 °C, and a total of 2176 effective sensing points over a\nsensing distance of 37.0 km by utilizing this coding scheme and link\noptimization techniques [1].\nLow-repetition-rate cyclic pulse coding scheme generates Simplex\ncoding-based cyclic coding sequences using an acousto-optic modulator\n(AOM), enabling pulses to be injected into the optical fiber periodically at a\nlow repetition rate. For example, in 2011, M. A. Soto, et al. combined the\nlow-repetition-rate quasi-periodic cyclic pulse coding with a high-power\nfiber laser, achieving a spatial resolution of 1.0 m, a temperature resolution\nof 3.0 °C, and 26,000 effective sensing points over a sensing distance of 26.0\nkm [2].\nPre-Shaped Simplex Coding scheme is based on simplex coding\ntechnology and adopts a linearly increasing profile to adjust pulse amplitude,\ncompensating for the amplitude variation caused by EDFA to suppress the\ntransient effect of the EDFA and improve system performance. For example,\nin 2017, J. B. Rosolem, et al. achieved a spatial resolution of 10.0 m, a\ntemperature resolution of 8.4 °C, and 6,200 effective sensing points over a\nsensing distance of 62.0 km by using the pre-shaped Simplex coding and a\ngain-controlled erbium-doped fiber amplifier [3].\nGenetic-optimised aperiodic coding scheme utilizes a distributed\ngenetic algorithm (DGA) to generate a single-sequence aperiodic code\n(GO-code), which is then converted into an optical pulse sequence and\ninjected into the optical fiber. For example, in 2020, X. Z. Sun, et al. achieved a spatial resolution of 1.0 m, a temperature resolution of 3.9 °C, and\n39,000 effective sensing points over a sensing distance of 39.0 km based on\nthe Genetic-optimised aperiodic coding scheme [4].\nDerived Sequences coding scheme addresses the transient effect of\nEDFA through a derived sequence decoding method, thereby enhancing the\nperformance of long-distance sensing. For instance, in 2022, D. D. Chai, et al.\nachieved a spatial resolution of 5.0 m, a temperature resolution of 2.5 °C, and\n8,800 effective sensing points over a sensing distance of 44.0 km based on the\nDerived Sequences coding scheme [5].\nEAC-coding scheme proposed in this manuscript incorporates a novel\npreprocessing framework for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered signals. This\nframework effectively suppresses the transient effect caused by EDFA and\nsignificantly enhances the fidelity and stability of the coded pulse sequence.\nSpecifically, the intrinsic gain provided by the pulse coding itself effectively\ncompensates for signal attenuation induced by long-distance transmission,\nthereby notably improving the base SNR. On this basis, a Haar wavelet\ndenoising algorithm is further integrated. For the residual noise in the signal\nafter encoding and decoding—noise with specific time-frequency domain\ncharacteristics (e.g., broadband noise or interference in specific frequency\nbands), the wavelet denoising algorithm can adaptively filter it out. This\nthree-fold synergistic mechanism, consisting of the preprocessing framework\ncompensating for EDFA fluctuation, coding gain suppressing transmission\nlosses, and wavelet transform finely removing residual noise, breaks through\nthe bottlenecks of traditional schemes in terms of SNR and effective sensing\ndistance. Over a sensing distance of 70.0 km, this technology achieves a\nspatial resolution of 1.58 m, a temperature resolution of 5.39 °C, and 44,303\neffective sensing points. To the best of our knowledge, the number of\neffective sensing points achieved by this scheme ranks the highest in the field\nof Raman distributed optical fiber sensing systems.\nTable 1. Sensing performance of various schemes.\n[1] J. Park, et al. Raman-based distributed temperature sensor with simplex\ncoding and link optimization. IEEE Photonics Technol. Lett. 18(17):\n1879-1881 (2006).\n[2] M. A. Soto, et al. Raman-based distributed temperature sensor with 1 m\nspatial resolution over 26 km SMF using low-repetition-rate cyclic pulse\ncoding. Opt. Lett. 36(13): 2557-2559 (2011).\n[3] J. B. Rosolem, et al. Raman DTS based on OTDR improved by using\ngain-controlled EDFA and pre-shaped simplex code. IEEE Sens. J. 17(11):\n3346-3353 (2017).\n[4] X. Z. Sun, et al. Genetic-optimised aperiodic code for distributed optical\nfibre sensors. Nat. Commun. 11(1), 5774 (2020).\n[5] D. D. Chai, et al. Derived sequences decoding approach for long-range\ndistributed temperature sensors. IEEE Sens. J. 23(3): 2204-2210 (2022).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the (unmodified manuscript) section of Introduction, page 2,\nleft column, paragraph 3, line 35, delete “The pulse coding\nscheme employs specific functional equations to encode detection\nsignals, and then decodes the collected Raman backscattered signals\nthrough a decoding program [21-22]. It increases the intensity of the\ndetection signals without the stimulated Raman generating nonlinear\neffects and thus improve the SNR of system. For example, Sun et al.\nproposed a genetic-optimised aperiodic coding scheme achieving a\nsensing spatial resolution of 1.0 m at the sensing distance of 39.0 km\n[23]. With the development of digital signal processing, various\ndenoising schemes are used in Raman distributed optical fiber\nsensing, including wavelet denoising algorithm and dynamic\nsampling-correction method [24-25]. For example, M. Yu, et al.\nproposed a dynamic sampling-correction scheme achieving a\nsensing distance of 20.0 km [26]. H. S. Pradhan, et al. proposed a\nFourier wavelet regularised deconvolution scheme achieving a\nsensing distance of 30.0 km with a spatial resolution of 3.0 m [27].\nFurthermore, the neural network scheme can learn the\ncharacteristic patterns of Raman scattering signals, perform\nconvolutional operations and subsequent processing on the input\nsignals to effectively identify and remove noise components, thereby\nimproving the SNR [28]. For example, Zhang et al. proposed a deep\n1-D denoising convolutional neural network scheme, which realized\na sensing distance of 10 km with a spatial resolution of 3 m [29].\nHowever, in large-scale engineering infrastructures, fiber\ndeployment typically adopts U-shaped or Hilbert-curve\nconfigurations, necessitating length of sensing fiber several times\ninfrastructures. Despite employing advanced denoising schemes in\nRaman distributed fiber sensing [30-32], achieving a further\nbreakthrough in sensing distance remains challenging under\nmeter-scale spatial resolution constraints.”\n2) In the section of Introduction, page 2, right column, paragraph 4,\nline 34, add “Pulse coding schemes have demonstrated significant\nadvantages in long-distance Raman distributed optical fiber sensing\nsystem. On one hand, by encoding the detection optical pulses, this\ntechnology can significantly increase the optical power injected into\nthe sensing fiber while avoiding fiber nonlinear effects, thereby\nenhancing the intensity of effective sensing signals at the level of\nsignal generation mechanism. On the other hand, at the data\nprocessing level, it leverages the separability between coded signals\nand uncoded noise to effectively suppress noise and improve the\nSNR of system.\nCurrently, pulse coding schemes applied in Raman distributed\noptical fiber sensing system are primarily classified into five\ncategories, which specifically include the Simplex coding scheme,\nPre-Shaped Simplex Coding scheme, low-repetition-rate cyclic\npulse coding scheme, Genetic-optimised aperiodic coding scheme,\nDerived Sequences coding scheme.\nSimplex coding scheme, as a linear coding technique based on\nHadamard matrix transformation, has its code length (in L bits) determining\nthe number of detection signals required (L groups). For instance, in\n2006, J. Park, et al. achieved a spatial resolution of 17.0\nm, a temperature resolution of 3.0 °C, and a total of 2176 effective\nsensing points over a sensing distance of 37.0 km by utilizing this\ncoding scheme and link optimization techniques [31].\nLow-repetition-rate cyclic pulse coding scheme generates\nSimplex coding-based cyclic coding sequences using an\nacousto-optic modulator (AOM), enabling pulses to be injected into\nthe optical fiber periodically at a low repetition rate. For example, in\n2011, M. A. Soto, et al. combined the low-repetition-rate\nquasi-periodic cyclic pulse coding with a high-power fiber laser,\nachieving a spatial resolution of 1.0 m, a temperature resolution of\n3.0 °C, and 26,000 effective sensing points over a sensing distance of\n26.0 km [27].\nPre-Shaped Simplex Coding scheme is based on simplex\ncoding technology and adopts a linearly increasing profile to adjust\npulse amplitude, compensating for the amplitude variation caused by\nEDFA to suppress the transient effect of the EDFA and improve\nsystem performance. For example, in 2017, J. B. Rosolem, et al.\nachieved a spatial resolution of 10.0 m, a temperature resolution of\n8.4 °C, and 6,200 effective sensing points over a sensing distance of\n62.0 km by using the pre-shaped Simplex coding and a\ngain-controlled erbium-doped fiber amplifier [32].\nGenetic-optimised aperiodic coding scheme utilizes a\ndistributed genetic algorithm (DGA) to generate a single-sequence\naperiodic code (GO-code), which is then converted into an optical\npulse sequence and injected into the optical fiber. For example, in\n2020, X. Z. Sun, et al. achieved a spatial resolution of 1.0 m, a\ntemperature resolution of 3.9 °C, and 39,000 effective sensing points\nover a sensing distance of 39.0 km based on the Genetic-optimised\naperiodic coding scheme [29].\nDerived Sequences coding scheme addresses the transient\neffect of EDFA through a derived sequence decoding method,\nthereby enhancing the performance of long-distance sensing. For\ninstance, in 2022, D. D. Chai, et al. achieved a spatial resolution of\n5.0 m, a temperature resolution of 2.5 °C, and 8,800 effective\nsensing points over a sensing distance of 44.0 km based on the\nDerived Sequences coding scheme [33].”\n6. The paper clearly states that the acquisition time for each Raman scattering signal\nis 63 minutes, and a total of four Raman scattering signals need to be acquired during\nthe decoding stage. Given the prolonged acquisition duration, how is the stability of\nthe experimental temperature and optical instruments performance ensured?\nReply: We would like to express our sincere gratitude to the reviewers\nfor their professional comments. In the proposed scheme of this manuscript,\nthe acquisition time for each Raman backscattered signal is 63 minutes.\nTherefore, in the experiment, the measurement time required for\ndemodulating the entire distributed temperature curve lasts for several hours.\nTo ensure the environmental temperature stability of the sensing fiber during\nthe long-term experiment, the entire 70.0 km sensing fiber is placed in an\nultra-clean constant-temperature laboratory, where the ambient temperature\nis maintained at 24.0±1.0 ℃. The FUT is placed in a high-precision\nconstant-temperature water bath with a temperature fluctuation of less than\n0.10 ℃. Thus, the above experimental setup can guarantee the temperature\nstability of the testing environment for the sensing fiber during long-term\nmeasurements. In addition, the experimental equipment used in this\nmanuscript, such as the detection light source, APD, and acquisition card,\ncan operate continuously for up to 2000 hours, which is sufficient to ensure\nlong-term continuous measurements.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental setup, page 9, right column,\nparagraph 3, line 20, add “To ensure the environmental\ntemperature stability of the sensing fiber during the long-term\nexperiment, the entire 70.0 km sensing fiber is placed in an\nultra-clean constant-temperature laboratory, where the ambient\ntemperature is maintained at 24.0±1.0 ℃. The FUT is placed in a\nhigh-precision constant-temperature water bath with a temperature\nfluctuation of less than 0.10 ℃. Thus, the above experimental setup\ncan guarantee the temperature stability of the testing environment\nfor the sensing fiber during long-term measurements.”\n7. Discrepancies in typography consistency are observed in Fig.3-Fig.7, particularly\nregarding the font sizes of axis captions and intra-figure text. For example, the axis\nlabels in Fig.6-Fig.7 and the text in Fig.7(b) exhibit notably larger font sizes\ncompared to other figures. It is recommended to standardize the typography across all\nfigures to ensure visual coherence and readability.\nReply: We would like to express our sincere gratitude to the reviewers for\ntheir valuable suggestions. Based on the reviewer’s comments, we have revised\nthe image formats of Fig. 6 and Fig. 7, and merged them into a single figure.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental results, page 14, change “Fig .6,\nFig .7” to “Fig .6”\nFig.6 Experimental comparison results of temperature sensing. (a1)\nTemperature demodulation results at room temperature based on single-pulse\nscheme. (a2) Temperature demodulation results at room temperature based on\ndistorted detection signals. (a3) Temperature demodulation results at room\ntemperature based on proposed EAC-coding scheme. (b1) SNR based on\nsingle-pulse scheme. (b2) SNR based on EAC-coding scheme (without\npre-processing). (b3) SNR based on proposed EAC-coding scheme. (c1)\nTemperature resolution based on single-pulse scheme. (c2) Temperature\nresolution based on EAC-coding scheme (without pre-processing). (c3)\nTemperature resolution based on proposed EAC-coding scheme. (d1) Temperature\ndemodulation results at 50 ℃ based on EAC-coding scheme and EAC-coding\nscheme (without pre-processing). (d2) Temperature demodulation results at 70 ℃\nbased on EAC-coding scheme and EAC-coding scheme (without pre-processing).\n(d3) Temperature demodulation results at 90 ℃ based on EAC-coding scheme and\nEAC-coding scheme (without pre-processing).\n8. Some of the chart labels are not clear enough. For example, the text in Fig.2 is\nundersized and the color contrast is insufficient, while the caption text in Fig.3(b)\nappears blurred. It is recommended that the format and size of all figures be\nstandardized to improve visual clarity and ensure that labels and annotations are clear\nand easy to read and consistent throughout the manuscript.\nReply: We would like to sincerely thank the reviewer for the valuable\nsuggestions. In accordance with the reviewers' comments, we have adjusted the\ntext size and color in Fig. 2, and modified the text size in Fig. 3 (b).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental setup, page 8, right column,\nchange “Fig .2” to “Fig .2”\nFig. 2. Experimental setup based on proposed EAC-coding scheme for Raman\ndistributed optical fiber sensing.\n2) In the section of Experimental setup, page 10, left column,\nchange “Fig .3” to “Fig .3”\nFig. 3. Timing of detection signals and autocorrelation function. (a1) Timing\nof the detection signal 𝒖 before and after transient effects. (a2) Timing of the\ndetection signal 𝒘̅ before and after transient effects. (a3) Timing of the\ndetection signal 𝒘 before and after transient effects. (a4) Timing of the\ndetection signal 𝒘̅ before and after transient effects. (b1) Autocorrelation\nfunction of the detection signals before transient effects. (b2) Autocorrelation\nfunction of the detection signals after transient effects.\nResponds to the reviewers’ comments:\nReviewer 2 (Comments to the Author):\nRecommendations for the Author(s):\nThe authors have demonstrated a record-long-distance distributed temperature sensing\nsystem based on Raman scattering. By combining Golay-encode autocorrelation\nprocessing, EDFA-transient-effect mitigation, and Haar wavelet denoising, the\nperformance of the sensing system has been significantly enhanced, achieving 1.58m\nspatial resolution and 0.88℃ measurement accuracy at a maximum sensing range of\n70km.This work represents a solid engineering breakthrough in long-distance\ndistributed temperature sensing and has the potential to generate societal impacts by\nproviding new capabilities to infrastructure monitoring. Therefore, this manuscript\ncan be accepted after being further improved by addressing the specific comments\nbelow.\nReply: Thank you very much for your evaluation of the content of this\nresearch and your constructive suggestions on the manuscript. We are also\nvery grateful to the reviewers for their recognition of the innovation of the\nproposal presented in this manuscript. These comments are of great value and\nwill be very helpful for revising and improving the manuscript as well as\nguiding the research work. We have carefully studied your comments and\nmade revisions accordingly, hoping that the revised version will meet your\nrequirements.\n1. The introduction should be significantly optimized to clearly state the key\ninnovation of this work. For example, the authors mentioned several existing\ndenoising techniques, but their limitations and the corresponding advantages of Haar\nwavelet denoising is not mentioned at all.\nReply: Thank you very much for the valuable and professional\ncomments from the reviewers, we fully concur with the reviewer's comments.\nBased on the reviewer's professional suggestions, we have made substantial\nrevisions to the introduction section, and three parts of revisions have been\nmade in the revised manuscript. First, we have supplemented the discussion\non the limitations of existing technologies in the Introduction and Discussion\nsection. Second, we have added content regarding the innovativeness of the\nEAC-coding technique in the last paragraph of the Introduction. Finally, we\nhave included the advantages of Haar wavelets in the Experimental Results\nsection. The specific supplementary content in the revised manuscript is as\nfollows.\n(1) Based on the professional suggestions of the reviewer, we have\nsupplemented the discussion on the limitations of existing technologies in\nthe Introduction and Discussion section. The specific supplementary\ncontent is as follows.\nAlgorithm denoising schemes aim to improve the SNR of the system by\nprocessing optical fiber scattering signals. Essentially derived from\nmathematical optimization theory, such schemes only denoise signals from\nthe perspective of signal processing without achieving breakthroughs in\nphysical mechanisms. Furthermore, they have limitations including\nparameter dependence and difficulty in preserving the true characteristics of\nsignals [1]. In addition, as one of the current mainstream denoising methods,\nconvolutional neural networks (CNNs) scheme is a typical data-driven\napproach. It optimizes model parameters using large-scale training datasets,\nwith the goal of achieving effective processing of test data. However, the\nperformance of this method is significantly constrained by the specificity of\ntraining data; when there is a notable distribution difference between test\nsignals and the training set, its effect on enhancing sensing performance will\nbe limited.\nIn contrast, pulse coding technology exhibits unique advantages in\nlong-distance Raman distributed optical fiber sensing, with its strengths lying\nin two aspects: physical mechanisms and information processing. At the\nphysical mechanism level, by encoding and modulating the detection optical\npulses, this technology significantly increases the optical power injected into\nthe sensing fiber without inducing fiber nonlinear effects, thereby enhancing\nthe intensity of the excited Raman scattering signals at the physical source [2].\nAt the signal processing level, pulse coding technology fully leverages the\nseparability between coded signals and background noise in the\ntime/frequency domain. Through matched filtering or demodulation\nalgorithms, it achieves effective noise suppression, thus improving the SNR\nat the signal processing level [3].\nCurrently, the pulse coding techniques applied in Raman distributed optical\nfiber sensing system mainly include the following: Simplex coding scheme,\nPre-Shaped Simplex coding scheme, Low-repetition-rate cyclic pulse coding\nscheme, Genetic-optimised aperiodic coding scheme, and\nDerived Sequences coding scheme. Their key performance indicators are\npresented in Table 2. Simplex coding scheme is a linear coding technique\nbased on Hadamard matrix transformation, where its code length (L bits)\ndetermines the number of detection signal groups required (L groups) [4]. The\nmain limitation of this scheme lies in the linear growth of data acquisition\nvolume and computational complexity with code length, which restricts its\npractical efficiency in applications requiring long code lengths and\nhigh-speed sensing. Low-repetition-rate cyclic pulse coding scheme\nutilizes an acousto-optic modulator (AOM) to generate Simplex\ncoding-based cyclic pulse sequences, enabling pulse injection at a low\nrepetition rate. This facilitates the injection of more energy into the sensing\nfiber, thereby enhancing the intensity of backscattered signals [2]. However,\nhigher pulse energy also makes it more likely to induce fiber nonlinear\neffects, and when approaching the stimulated scattering threshold, it restricts\nthe system’s sensing distance and SNR performance. Pre-Shaped Simplex\ncoding scheme introduces linear profile shaping of pulse amplitude based on\nthe Simplex code to compensate for the amplitude fluctuation of pulses\ncaused by EDFA, thereby improving system stability [5]. Although this\nscheme effectively suppresses the transient response of the EDFA at the\nhardware level, its hardware structure is more complex, leading to a\nsignificant increase in implementation cost. Genetic-optimised aperiodic\ncoding scheme generates aperiodic sequences (GO-code) through\noptimization via a distributed genetic algorithm (DGA), which are then\nconverted into optical pulse sequences and injected into the sensing fiber [3].\nThe core challenge of this scheme lies in its high dependence on optimization\nalgorithms to search for the optimal code, which typically requires\nsubstantial computational resources and iterative testing. Derived Sequences\ncoding scheme suppresses the impact of EDFA transient effects on\nlong-distance sensing by introducing a specific derived decoding strategy [6].\nHowever, its decoding process imposes a heavy computational burden, and\nthe core algorithm involves high-complexity matrix operations, making it\ndifficult to meet real-time requirements.\nCurrently, existing pulse coding techniques in Raman distributed optical\nfiber sensing remain constrained by several prevalent bottlenecks: high\nhardware implementation complexity, excessive computational overhead in\nencoding and decoding, limited nonlinear effect suppression capability, and\ninadequate resistance to signal distortion coupled with poor stability during\nlong-distance transmission. Collectively, these factors constrain the system’s\napplication potential in high-performance scenarios—including low SNR\nenvironments and long-distance sensing applications.\nTo address the aforementioned issues, an Enhanced anti-distortion\ncoding (EAC-coding) scheme is proposed in this manuscript. This scheme\neffectively overcomes the trade-off dilemma among SNR, sensing distance,\nand hardware cost in traditional methods through a three-fold synergistic\nmechanism: compensating for EDFA fluctuation via a preprocessing\nframework, suppressing transmission losses through coding gain, and finely\nremoving residual noise using wavelet transform. While maintaining\nrelatively low complexity, the EAC-coding scheme significantly enhances the\nanti-distortion capability and adaptability of the system, providing a new\nsolution for long-distance, high-performance Raman distributed optical fiber\nsensing.\nTable 2. Sensing performance of various coding schemes.\n(2) Based on the professional suggestions of the reviewer, we have\nadded content regarding the innovativeness of the EAC-coding\ntechnique in the Introduction section. The specific supplementary\ncontent is as follows.\nEAC-coding scheme proposed in this manuscript incorporates a novel\npreprocessing framework for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered signals. The\npreprocessing architecture for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction in this scheme can effectively suppress\nthe transient effects introduced by EDFA, thereby significantly improving the\namplitude fidelity and temporal stability of the encoded pulse sequence. This\ninnovative active reconstruction mechanism in the signal domain, which is\nbased on analyzing the waveforms of Raman backscattered signals via\nforward/inverse Fourier transforms, directly eliminates the phenomenon of\ndetection pulse distortion existing in traditional demodulation schemes. The\nscope of action of the EAC-coding scheme encompasses two key aspects:\nspecifically, one is addressing the fundamental limitation of detection signal\ndistortion through physical-layer waveform reconstruction, and the other is\nperforming correlation operations between the proposed coding sequence and\nthe reconstructed Raman signal to restore the ideal cross-correlation\ncharacteristics of Golay sequences, and achieve a theoretical gain value,\nthereby breaking through the SNR-distance trade-off limit. It achieves the\ncoordinated optimization of “waveform correction, correlation characteristic\nrestoration, signal intensity enhancement”, laying a physical layer foundation\nfor long-distance sensing.\nFurthermore, the proposed EAC-coding scheme features a\nsynergistically enhanced two-stage noise suppression mechanism,\ndemonstrating innovations in multi-level joint denoising.\nFirst, EAC-coding scheme enhances the SNR of sensing signals through\nits inherent coding gain. Based on the cross-correlation characteristics of its\nsequence design, this coding scheme provides a significant inherent gain,\nwhich compensates for signal attenuation caused by long-distance\ntransmission and effectively improves the system's baseline SNR.\nFurthermore, this mechanism not only significantly boosts optical power but\nalso leverages the irrelevance between the decoding algorithm and incoherent\nnoise to achieve preliminary suppression of transmission link losses at the\nencoding-decoding level.\nSecond, aiming at the residual noise with specific time-frequency\ndomain distribution characteristics in the decoded signal, this scheme further\nintroduces Haar wavelet transform for adaptive noise filtering. The\nmulti-resolution analysis capability of the Haar wavelet enables accurate\ncapture of the local time-frequency features of noise. By performing sparse\nrepresentation of the signal at different scales (corresponding to different\nfrequency bands) and time-domain positions, it achieves effective separation\nbetween useful signals and non-stationary noise components. While\npreserving the key details of the distributed temperature signal, this method\nefficiently eliminates residual noise, significantly enhancing the clarity of the\nsignal in the time-frequency domain and the overall measurement accuracy\nof the system.\nThis three-fold synergistic mechanism, consisting of the preprocessing\nframework compensating for EDFA fluctuation, coding gain suppressing\ntransmission losses, and wavelet transform finely removing residual noise,\nsystematically breaks through the bottlenecks of traditional schemes in terms\nof SNR and sensing distance, providing a novel decoding framework for\nlong-distance and high-precision Raman distributed optical fiber sensing.\n(3) Based on the professional suggestions of the reviewer, we have\nincluded the advantages of Haar wavelets in the Experimental Results\nsection. The specific supplementary content is as follows.\nIn this study, a denoising algorithm based on the Haar wavelet is\nadopted to process distributed temperature sensing signals with abrupt\nchange characteristics. The inherent step-like form of the Haar wavelet basis\nfunction endows it with excellent feature extraction capability for singular\npoints in the signal, especially for the abrupt temperature field change\nregions along the sensing fiber. Theoretical analysis indicates that the Haar\nwavelet transform tends to represent abrupt signals as prominent wavelet\ncoefficients, while its inverse transform process can effectively reconstruct\nsignals with step characteristics. This property is crucial in the denoising\nprocess of Raman distributed optical fiber sensing technology: through\ntargeted threshold processing, it can not only effectively suppress noise but\nalso maximize the retention of the signal structure that characterizes abrupt\ntemperature changes, thereby significantly alleviating the deterioration of the\nsystem's spatial resolution performance caused by traditional denoising\nmethods.\n[1] L. Xu, et al. RDTS noise reduction method based on\nICEEMDAN-FE-WSTD. IEEE Sens. J. 22(18): 17854-17863 (2022).\n[2] M. A. Soto, et al. Raman-based distributed temperature sensor with 1 m\nspatial resolution over 26 km SMF using low-repetition-rate cyclic pulse\ncoding. Opt. Lett. 36(13): 2557-2559 (2011).\n[3] X. Z. Sun, et al. Genetic-optimised aperiodic code for distributed optical\nfibre sensors. Nat. Commun. 11(1), 5774 (2020).\n[4] J. Park, et al. Raman-based distributed temperature sensor with simplex\ncoding and link optimization. IEEE Photonics Technol. Lett. 18(17):\n1879-1881 (2006).\n[5] J. B. Rosolem, et al. Raman DTS based on OTDR improved by using\ngain-controlled EDFA and pre-shaped simplex code. IEEE Sens. J. 17(11):\n3346-3353 (2017).\n[6] D. D. Chai, et al. Derived sequences decoding approach for long-range\ndistributed temperature sensors. IEEE Sens. J. 23(3): 2204-2210 (2022).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Introduction, page 2, right column, paragraph 2,\nline 3, add “Algorithm denoising schemes aim to improve the SNR\nof the system by processing optical fiber scattering signals. For\nexample, M. Yu, et al. proposed a dynamic sampling-correction\nscheme achieving a sensing distance of 20.0 km [23]. H. S. Pradhan,\net al. proposed a Fourier wavelet regularised deconvolution scheme\nachieving a sensing distance of 30.0 km with a spatial resolution of\n3.0 m [24]. Essentially derived from mathematical optimization\ntheory, such schemes only denoise signals from the perspective of\nsignal processing without achieving breakthroughs in physical\nmechanisms. Furthermore, they have limitations including parameter\ndependence and difficulty in preserving the true characteristics of\nsignals [30].\nIn addition, as one of the current mainstream denoising\nmethods, convolutional neural networks (CNNs) scheme is a typical\ndata-driven approach. It optimizes model parameters using\nlarge-scale training datasets, with the goal of achieving effective\nprocessing of test data. For example, Z. Zhang, et al. proposed a\ndeep 1-D denoising convolutional neural network scheme, which\nrealized a sensing distance of 10 km with a spatial resolution of 3 m\n[26]. However, the performance of this method is significantly\nconstrained by the specificity of training data; when there is a\nnotable distribution difference between test signals and the training\nset, its effect on enhancing sensing performance will be limited.”\n2) In the (unmodified manuscript) section of Introduction, page 3,\nleft column, paragraph 2, line 3, delete“ In this work, an enhanced\nautocorrelation pulse coding (EAC-coding) scheme is proposed,\nwhich introduces Golay complementary sequences into Raman\ndistributed optical fiber sensing, and at the same time restores the\nautocorrelation which is destroyed by the transient effects of\nerbium-doped fiber amplifier (EDFA) by preprocessing the Raman\nbackscattered signals for analysis and waveform-reconstruction. The\nproposed scheme further incorporates Haar wavelet denoising\nalgorithm to enhance system performance. In the experiment, a\nRaman distributed optical fiber sensing with sensing distance of 70.0\nkm, spatial resolution of 1.58 m and temperature resolution of 5.39 ℃\nis achieved, which provides a new solution for the research of\nlong-distance Raman distributed optical fiber sensing.”\n3) In the section of Introduction, page 4, left column, paragraph 4,\nline 34, add “Currently, existing pulse coding techniques in Raman\ndistributed optical fiber sensing remain constrained by several\nprevalent bottlenecks: high hardware implementation complexity,\nexcessive computational overhead in encoding and decoding, limited\nnonlinear effect suppression capability, and inadequate resistance to\nsignal distortion coupled with poor stability during long-distance\ntransmission. Collectively, these factors constrain the system’s\napplication potential in high-performance scenarios—including low\nSNR environments and long-distance sensing applications.\nTo address the aforementioned issues, an Enhanced\nanti-distortion coding (EAC-coding) scheme is proposed in this\npaper. This scheme effectively overcomes the trade-off dilemma\namong SNR, sensing distance, and hardware cost in traditional\nmethods through a three-fold synergistic mechanism: compensating\nfor EDFA fluctuation via a preprocessing framework, suppressing\ntransmission losses through coding gain, and finely removing\nresidual noise using wavelet transform. While maintaining relatively\nlow complexity, the EAC-coding scheme significantly enhances the\nanti-distortion capability and adaptability of the system, providing a\nnew solution for long-distance, high-performance Raman distributed\noptical fiber sensing. Experimental results demonstrate that at an\nultra-long distance of 70.0 km, the system achieves a spatial\nresolution of 1.58 m and a temperature resolution of 5.39 ℃, with\nthe number of effective sensing points reaching 44,303. To the best\nof our knowledge, this number of effective sensing points represents\nthe highest level in the field of Raman distributed optical fiber\nsensing. In addition, the preprocessing architecture within\nEAC-coding (autocorrelation characteristic analysis, waveform\nanalysis and reconstruction of Raman backscattered signals) significantly\nenhances the temporal fidelity and transmission stability of encoded\nsequences by dynamically compensating for EDFA transient gain\nfluctuation. This further improves the SNR and temperature\nmeasurement accuracy performance, enabling the temperature\nmeasurement accuracy to reach 0.91 ℃, verifying the engineering\nfeasibility of the scheme.”\n4) In the (unmodified manuscript) section of Experimental results,\npage 10, right column, paragraph 2, line 29, delete “Raman\ndistributed optical fiber sensing has emerged as a pivotal technology\nfor continuous temperature monitoring in long-range infrastructure\nand environmental applications. However, its practical\nimplementation over distances exceeding 30 km has been\nfundamentally hindered by the inherently low signal-to-noise ratio\n(SNR) of Raman scattering signals, which creates a critical trade-off\nbetween sensing distance and spatial resolution. In this study, we\npresent a novel Raman distributed optical fiber sensing system\nutilizing the proposed EAC-coding scheme, which effectively\nsuppresses transient effects and significantly enhances the SNR of\nsystem while incorporating Haar wavelet. This system enables\nlong-distance Raman distributed temperature measurement with\nhigh spatial resolution, achieving precise temperature demodulation\nand accurate identification of FUT position and length. The\nexperimental results demonstrate that the proposed scheme achieves\na spatial resolution of 1.58 m, temperature resolution of 5.39 ℃, and\ntemperature measurement accuracy of 0.88 ℃ at the sensing\ndistance of 70.0 km, establishing a new approach for long-distance\nRaman distributed optical fiber sensing system. Future research will\nintegrate more advanced denoising techniques to extend the system's\nsensing distance while preserving its spatial resolution capabilities.”\n5) In the section of Experimental results, page 18, left column,\nparagraph 2, line 10, add “EAC-coding scheme proposed in this\npaper incorporates a novel preprocessing framework for\nautocorrelation characteristic analysis, waveform analysis and\nreconstruction of Raman backscattered signals. The preprocessing\narchitecture for autocorrelation characteristic analysis, waveform\nanalysis and reconstruction in this scheme can effectively suppress\nthe transient effects introduced by EDFA, thereby significantly\nimproving the amplitude fidelity and temporal stability of the\nencoded pulse sequence. This innovative active reconstruction\nmechanism in the signal domain, which is based on analyzing the\nwaveforms of Raman backscattered signals via forward/inverse\nFourier transforms, directly eliminates the phenomenon of detection\npulse distortion existing in traditional demodulation schemes. The\nscope of action of the EAC-coding scheme encompasses two key\naspects: specifically, one is addressing the fundamental limitation of\ndetection signal distortion through physical-layer waveform\nreconstruction, and the other is performing correlation operations\nbetween the proposed coding sequence and the reconstructed Raman\nsignal to restore the ideal cross-correlation characteristics of Golay\nsequences, and achieve a theoretical gain value, thereby breaking\nthrough the SNR-distance trade-off limit. It achieves the coordinated\noptimization of “waveform correction, correlation characteristic\nrestoration, signal intensity enhancement”, laying a physical layer\nfoundation for long-distance sensing.\nFurthermore, the proposed EAC-coding scheme features a\nsynergistically enhanced two-stage noise suppression mechanism,\ndemonstrating innovations in multi-level joint denoising.\nFirst, EAC-coding scheme enhances the SNR of sensing signals\nthrough its inherent coding gain. Based on the cross-correlation\ncharacteristics of its sequence design, this coding scheme provides a\nsignificant inherent gain, which compensates for signal attenuation\ncaused by long-distance transmission and effectively improves the\nsystem's baseline SNR. Furthermore, this mechanism not only\nsignificantly boosts optical power but also leverages the irrelevance\nbetween the decoding algorithm and incoherent noise to achieve\npreliminary suppression of transmission link losses at the\nencoding-decoding level.\nSecond, aiming at the residual noise with specific\ntime-frequency domain distribution characteristics in the decoded\nsignal, this scheme further introduces Haar wavelet transform for\nadaptive noise filtering. The multi-resolution analysis capability of\nthe Haar wavelet enables accurate capture of the local\ntime-frequency features of noise. By performing sparse\nrepresentation of the signal at different scales (corresponding to\ndifferent frequency bands) and time-domain positions, it achieves\neffective separation between useful signals and non-stationary noise\ncomponents. While preserving the key details of the distributed\ntemperature signal, this method efficiently eliminates residual noise,\nsignificantly enhancing the clarity of the signal in the\ntime-frequency domain and the overall measurement accuracy of the\nsystem.\nThis three-fold synergistic mechanism, consisting of the\npreprocessing framework compensating for EDFA fluctuation,\ncoding gain suppressing transmission losses, and wavelet transform\nfinely removing residual noise, systematically breaks through the\nbottlenecks of traditional schemes in terms of SNR and sensing\ndistance, providing a novel decoding framework for long-distance\nand high-precision Raman distributed optical fiber sensing.”\n6) In the section of Experimental results, page 13, left column,\nparagraph 2, line 18, add “In this study, a denoising algorithm\nbased on the Haar wavelet is adopted to process distributed\ntemperature sensing signals with abrupt change characteristics. The\ninherent step-like form of the Haar wavelet basis function endows it\nwith excellent feature extraction capability for singular points in the\nsignal, especially for the abrupt temperature field change regions\nalong the sensing fiber.”\n7) In the section of Introduction, page 3, left column, paragraph 3,\nline 27, add “The main limitation of this scheme lies in the linear\ngrowth of data acquisition volume and computational complexity\nwith code length, which restricts its practical efficiency in\napplications requiring long code lengths and high-speed sensing.”\n8) In the section of Introduction, page 3, right column, paragraph 1,\nline 9, add “However, higher pulse energy also makes it more likely\nto induce fiber nonlinear effects, and when approaching the\nstimulated scattering threshold, it restricts the system’s sensing\ndistance and SNR performance.”\n9) In the section of Introduction, page 3, right column, paragraph 2,\nline 25, add “Although this scheme effectively suppresses the\ntransient response of the EDFA at the hardware level, its hardware\nstructure is more complex, leading to a significant increase in\nimplementation cost.”\n10) In the section of Introduction, page 4, left column, paragraph 1,\nline 3, add “The core challenge of this scheme lies in its high\ndependence on optimization algorithms to search for the optimal\ncode, which typically requires substantial computational resources\nand iterative testing.”\n11) In the section of Introduction, page 4, left column, paragraph 2,\nline 17, add “However, this scheme’s decoding process imposes a\nheavy computational burden, and the core algorithm involves\nhigh-complexity matrix operations, making it difficult to meet\nreal-time requirements.”\n2. As the core innovation of this work, the uniqueness of Golay-encode\nautocorrelation processing is insufficiently explained. How does it compare\nquantitatively to other well established coding methods such as Simplex coding and\ngenetic-optimized aperiodic coding? For example, maybe the discussion can be made\nfrom the perspective of coding gain and measurement time. After all, the physical\nreason that the record-breaking performance can be achieved should be explicitly\npointed out.\nReply: We sincerely appreciate the reviewers' professional and valuable\nsuggestions. We believe that the innovation of this manuscript has been\nsignificantly enhanced after revisions based on your comments. In\naccordance with the reviewers' professional advice, we have compared our\nproposed scheme with other coding methods such as simplex coding and\nGenetic-optimised aperiodic coding in terms of coding gain, measurement\ntime, and system complexity. The specific revisions are as follows.\nIn terms of coding gain, the EAC-coding scheme proposed in this manuscript\nexhibits significant advantages in SNR improvement. The core of this scheme lies in the analysis and accurate reconstruction of the waveform of Raman backscattered signals, which effectively compensates for the distortion of detection signals caused by transient effects. This mechanism enables EAC-coding to overcome the performance bottleneck of traditional derived sequences coding schemes induced by signal distortion, thereby achieving a coding gain that is closer to the theoretical limit. Specifically, existing derived sequences coding schemes construct coding sequences based on Golay complementary sequences and perform correlation decoding using their derived sequences. The upper limit of their theoretical coding gain is √L/2 (where L denotes the length of the coding sequence) [1]. However, due to the unavoidable distortion (especially transient distortion) in actual detection signals, the results of their correlation operations are degraded, leading to a significant gap between the actual coding gain obtained and this theoretical value. In contrast, the EAC-coding scheme, through the autocorrelation characteristic analysis, waveform analysis and reconstruction of Raman backscattered signals, significantly suppresses the impact of transient distortion on the detected waveform, allowing its coding gain to approach the theoretical upper limit of √L/2. Benefiting from this, the proposed system ultimately achieves the capability of temperature sensing in a long-distance Raman distributed optical fiber sensing system with a sensing distance of 70.0 km.\nIn terms of measurement time, the core advantage of the EAC-coding\nscheme stems from its extremely low decoding computational complexity.\nThis scheme achieves signal reconstruction solely through Fourier transform,\nwhich significantly reduces the computational cost and time delay of\nreal-time data processing, thereby effectively improving the overall response\nspeed of the system. Details are as follows: For a Simplex code with a code\nlength of L, it is necessary to inject L groups of detection signals into the\noptical fiber and collect L groups of Raman backscattered signals; its\ntheoretical minimum acquisition time is given by T =L×t (where t\nSimplex\ndenotes the acquisition time of a single group of Raman backscattered curves)\n[2]. Although Genetic-optimised aperiodic coding only requires injecting one\ngroup of detection signals into the optical fiber, it necessitates additional time\nto design coding sequences based on the distributed genetic algorithm.\nDerived Sequences coding requires injecting 4 groups of detection signals\ninto the optical fiber (theoretical acquisition time of 4t), and during the\ndecoding stage, it involves complex procedures such as extracting the\nattenuation envelope, establishing a compensation model, and solving the\ncompensation envelope via matrix operations—all of which increase the time\ncost of the decoding process. The EAC-coding scheme proposed in this\nmanuscript performs coding based on Golay complementary sequences, with\na theoretical acquisition time of 4t, and only needs Fourier transform to\ncomplete the analysis and reconstruction of the Raman backscattered signal\nwaveform. This significant efficiency improvement at the algorithm level\ngreatly reduces the delay in real-time data processing, effectively enhances\nthe system response speed, and provides crucial real-time performance\nguarantees for the final realization of a 70.0 km long-distance Raman\ndistributed optical fiber sensing system.\nIn terms of system complexity, the core innovation of the EAC-coding\nscheme lies in achieving a high degree of simplification in the decoding\nprocess through algorithm optimization, while keeping the hardware\narchitecture unchanged. This scheme only needs to perform efficient Fourier\ntransform operations to complete signal reconstruction, which significantly\nreduces the algorithmic complexity and computational burden of real-time\ndata processing. The specific reasons are as follows. Simplex coding scheme\nrequires the injection of L groups of detection signals, resulting in a long\nacquisition time and a large volume of raw data. This not only imposes high\nrequirements on hardware performance (such as data acquisition rate and\nstorage capacity) and long-term stability, but also the large-scale data\nprocessing involved in its decoding process significantly increases the\ncomputational complexity. Genetic-optimised aperiodic coding scheme\ngreatly shortens the acquisition time without increasing hardware costs.\nHowever, due to its unique design, it is necessary to design coding sequences\nbased on a distributed genetic algorithm and conduct extensive tests to find\nthe optimal coding sequence. Derived sequences coding scheme also does\nnot require additional hardware overhead. However, this scheme introduces\nhigh computational complexity in the decoding stage, as it relies on\ncomputationally expensive matrix operations to generate and process derived\nsequences.\n[1] D. D. Chai, et al. Derived sequences decoding approach for long-range\ndistributed temperature sensors. IEEE Sens. J. 23(3): 2204-2210 (2022).\n[2] J. Park, et al. Raman-based distributed temperature sensor with simplex\ncoding and link optimization. IEEE Photonics Technol. Lett. 18(17):\n1879-1881 (2006).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Discussion, page 19, right column, paragraph 4,\nline 7, add “Currently, the pulse coding techniques applied in\nRaman distributed optical fiber sensing system mainly include the\nfollowing: Simplex coding scheme, Pre-Shaped Simplex coding\nscheme, Low-repetition-rate cyclic pulse coding scheme,\nGenetic-optimised aperiodic coding scheme, and Derived Sequences\ncoding scheme. Their key performance indicators are presented in\nTable 2.\nTable 2. Sensing performance of various coding schemes.\nWe have compared our proposed scheme with other coding\nmethods such as simplex coding and Genetic-optimised aperiodic\ncoding in terms of coding gain, measurement time, and system\ncomplexity. The specific revisions are as follows.\nIn terms of coding gain, the EAC-coding scheme proposed in\nthis paper exhibits significant advantages in SNR improvement. The\ncore of this scheme lies in the analysis and accurate reconstruction\nof the waveform of Raman backscattered signals, which effectively\ncompensates for the detection signals distortion caused by the\ntransient effects of the system. This mechanism enables EAC-coding\nto overcome the performance bottleneck of traditional derived\nsequences coding schemes induced by signals distortion, achieving a\ncoding gain closer to the theoretical limit. Specifically, existing\nderived sequence coding scheme construct coding sequences based\non Golay complementary sequences and perform correlation\ndecoding using their derived sequences. The upper limit of their\ntheoretical coding gain is √L/2 (where L denotes the length of the\ncoding sequence). However, due to the unavoidable distortion\n(especially transient distortion) in actual detection signals, the\nresults of their correlation operations deteriorate, leading to a\nsignificant gap between the actually achieved coding gain and this\ntheoretical value. In contrast, the EAC-coding scheme, through the\naforementioned signals analysis and reconstruction mechanism,\nsignificantly suppresses the impact of transient distortion on the\ndetection signals waveform, thereby enabling its coding gain to\napproach the theoretical upper limit of √L/2. Benefiting from this,\nthe proposed system ultimately achieves temperature sensing\ncapability in a long-distance Raman distributed optical fiber sensing\nsystem with a sensing distance of 70.0 km.\nIn terms of measurement time, the core advantage of the\nEAC-coding scheme stems from its extremely low decoding\ncomputational complexity. This scheme achieves signals\nreconstruction solely through Fourier transform, which significantly\nreduces the computational cost and time delay of real-time data\nprocessing, thereby effectively improving the overall response speed\nof the system. Specifically, for a Simplex code with length L, it is\nnecessary to inject L groups of detection signals into the optical fiber\nand collect L groups of Raman backscattered signals, with its\ntheoretical minimum acquisition time being T =L×t (where t\nSimplex\ndenotes the acquisition time of one group of Raman backscattered\ncurves). Although the Genetic-optimised aperiodic coding scheme\nonly requires injecting one group of detection signals into the optical\nfiber, it needs additional time to design the coding sequence based\non the distributed genetic algorithm. The Derived sequences coding\nscheme requires injecting 4 groups of detection signals into the\noptical fiber, with a theoretical acquisition time of 4t. However, in\nthe decoding stage, it involves complex steps such as extracting the\nattenuation envelope, establishing a compensation model, and\nsolving the compensation envelope via matrix operations, which\nincreases the time cost of the decoding process. The EAC-coding\nscheme proposed in this paper performs encoding based on Golay\ncomplementary sequences, with a theoretical acquisition time of 4t,\nand only needs Fourier transform to complete the analysis and\nreconstruction of the Raman backscattered signals waveform. This\nsignificant efficiency improvement at the algorithm level greatly\nreduces the real-time data processing delay and effectively enhances\nthe system response speed, providing crucial real-time guarantee for\nthe final realization of temperature sensing in a 70.0 km\nlong-distance Raman distributed optical fiber sensing system.\nIn terms of system complexity, the core innovation of the\nEAC-coding scheme lies in achieving a high degree of\nsimplification in the decoding process through algorithm\noptimization, while keeping the hardware architecture unchanged.\nThis scheme only needs to perform efficient Fourier transform\noperations to complete signal reconstruction, which significantly\nreduces the algorithmic complexity and computational burden of\nreal-time data processing. The specific reasons are as follows.\nSimplex coding scheme requires the injection of L groups of detection\nsignals, resulting in a long acquisition time and a large volume of raw data.\nThis not only imposes high requirements on hardware performance\n(such as data acquisition rate and storage capacity) and long-term\nstability, but also the large-scale data processing involved in its\ndecoding process significantly increases the computational complexity.\nGenetic-optimised aperiodic coding scheme greatly shortens the\nacquisition time without increasing hardware costs. However, due to\nits unique design, it is necessary to design coding sequences based on\na distributed genetic algorithm and conduct extensive tests to find\nthe optimal coding sequence. Derived sequences coding scheme also\ndoes not require additional hardware overhead. However, this scheme\nintroduces high computational complexity in the decoding stage, as it\nrelies on computationally expensive matrix operations to generate and\nprocess derived sequences.\nEAC-coding scheme proposed in this paper incorporates a\nnovel preprocessing framework for autocorrelation characteristic\nanalysis, waveform analysis and reconstruction of Raman\nbackscattered signals. This framework significantly improves the\nfidelity and transmission stability of the encoded pulse sequence by\ndynamically compensating for the transient gain fluctuation of\nEDFA. This technology leverages the inherent gain of EAC-coding\npulse coding to effectively offset fiber scattering attenuation during\n70.0 km long-distance transmission, achieving a significant\nimprovement in the baseline SNR. On this basis, a two-stage noise\nsuppression method is further constructed. The first-stage processing\ninvolves compensating for signal attenuation using the theoretical\ncoding gain of EAC-coding. For the second-stage processing, a Haar\nwavelet denoising algorithm is adopted. Its step-matching\ncharacteristic enables accurate extraction of the abrupt temperature\nchange features of the sensing fiber and adaptive filtering of the\nresidual time/frequency domain coupled noise in the decoded signal.\nThis three-fold synergistic mechanism, consisting of the\npreprocessing framework compensating for EDFA fluctuation,\ncoding gain suppressing transmission losses, and wavelet transform\nfinely removing residual noise, breaks through the theoretical\ntrade-off bottleneck between SNR and sensing distance in traditional\nschemes. Experiment results indicate that, at an ultra-long distance of\n70.0 km, this scheme can achieve a spatial resolution of 1.58 m, a\ntemperature resolution of 5.39 °C, and an effective number of\nsensing points reaching 44,303, verifying the engineering feasibility\nof the scheme. To the best of our knowledge, the number of\neffective sensing points achieved by this scheme ranks the highest in\nthe field of Raman distributed optical fiber sensing systems.”\n3. To let the reader to better evaluate the performance in this work, a quantitative and\nfair comparison with the state of the art should be made. If possible, a figure of merit\nshould be given that normalizes the measurement time, considering that the\nperformance in this work is obtained over one hour.\nReply: Thank you for your valuable suggestions, which are of great\nhelp in enhancing the innovation of this manuscript and guiding the research\nwork to be carried out in the future. Based on the reviewer's professional\nsuggestions, we have quantitatively analyzed the measurement time in the\ndiscussion section. Furthermore, we have compared and elaborated on the\nkey performance indicators of our proposed scheme with those of existing\ncoding techniques. The revised content is as follows.\nCurrently, in the field of Raman distributed optical fiber sensing, a\nperformance comparison between conventional coding schemes and the\nproposed EAC-coding scheme is presented in Table 3.\nSimplex coding scheme, as a linear coding technique based on\nHadamard matrix transformation, has its code length (in L bits) determining\nthe number of detection signals required (L groups). By leveraging the\nSimplex coding and link optimization technology, a spatial resolution of 17.0\nm, a temperature resolution of 3.0 °C, and an effective number of sensing\npoints of 2176 have been achieved at a sensing distance of 37.0 km [1].\nLow-repetition-rate cyclic pulse coding scheme generates Simplex\ncoding-based cyclic coding sequences using an acousto-optic modulator\n(AOM), enabling pulses to be injected into the optical fiber periodically at a\nlow repetition rate. The combination of low-repetition-rate cyclic pulse\ncoding and a high-power fiber laser achieves a spatial resolution of 1.0 m, a\ntemperature resolution of 3.0 °C, an effective number of sensing points of\n26,000, and a measurement time of 30 s at a sensing distance of 26.0 km [2].\nPre-Shaped Simplex Coding scheme is based on simplex coding\ntechnology and adopts a linearly increasing profile to adjust pulse amplitude,\ncompensating for the amplitude variation caused by EDFA to suppress the\ntransient effect of EDFA and improve system performance. Based on\npre-shaped Simplex coding and a gain-controlled EDFA, a spatial resolution\nof 10.0 m, a temperature resolution of 8.4 °C, and an effective number of\nsensing points of 6,200 have been achieved at a sensing distance of 62.0 km\n[3].\nGenetic-optimised aperiodic coding scheme utilizes a distributed\ngenetic algorithm (DGA) to generate a single-sequence aperiodic code\n(GO-code), which is then converted into an optical pulse sequence and\ninjected into the optical fiber. This scheme achieved a spatial resolution of\n1.0 m, a temperature resolution of 3.9 °C, an effective number of sensing\npoints of 39,000, and a measurement time of 13.6 min at a sensing distance\nof 39.0 km [4].\nDerived Sequences coding scheme addresses the transient effect of\nEDFA through a derived sequence decoding method, thereby enhancing the\nperformance of long-distance sensing. Based on the Derived Sequences\ncoding scheme, a spatial resolution of 5.0 m, a temperature resolution of 2.5 °C, and an effective number of sensing points of 8,800 have been\nachieved at a sensing distance of 44.0 km [5].\nEAC-coding scheme proposed in this manuscript incorporates a novel\npreprocessing framework for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered signals. This\nframework significantly improves the fidelity and transmission stability of the\nencoded pulse sequence by dynamically compensating for the transient\ngain fluctuation of EDFA. This technology leverages the inherent gain of\nEAC-coding pulse coding to effectively offset fiber scattering attenuation\nduring 70.0 km long-distance transmission, achieving a significant\nimprovement in the baseline SNR. On this basis, a two-stage noise\nsuppression method is further constructed. The first-stage processing\ninvolves compensating for signal attenuation using the theoretical coding\ngain of EAC-coding. For the second-stage processing, a Haar wavelet\ndenoising algorithm is adopted. Its step-matching characteristic enables\naccurate extraction of the abrupt temperature change features of the sensing\nfiber and adaptive filtering of the residual time/frequency domain coupled\nnoise in the decoded signal. This three-fold synergistic mechanism, consisting of the\npreprocessing framework compensating for EDFA\nfluctuation, coding gain suppressing transmission losses, and wavelet\ntransform finely removing residual noise, breaks through the theoretical\ntrade-off bottleneck between SNR and sensing distance in traditional\nschemes. Experiment results indicate that, at an ultra-long distance of 70.0\nkm, this scheme can achieve a spatial resolution of 1.58 m, a temperature\nresolution of 5.39 °C, and an effective number of sensing points reaching\n44,303, verifying the engineering feasibility of the scheme.\nFurthermore, the measurement time of the scheme proposed in this\nmanuscript is mainly limited by the massive data volume (with the effective\nnumber of sensing points reaching 44,303) and the hardware accumulation\nprocessing time of the acquisition card, which are caused by its long sensing\ndistance and high spatial resolution—rather than the complexity of its\nprocessing architecture. The current measurement time (252 min) is\nconstrained by the processing capability of the data acquisition card\n(acquisition rate: 1.0 GSa/s; storage depth: 512 Mpts). The massive data\nvolume (approximately 700 k points per frame corresponding to a 70.0 km\nsensing distance) exceeds the on-board real-time processing limit. In the\nfuture, high-performance acquisition cards will be upgraded to optimize the\ndata processing pipeline, thereby eliminating the delay deterioration caused\nby hardware bottlenecks.\nTable 3. Sensing performance of various coding schemes.\n[1] J. Park, et al. Raman-based distributed temperature sensor with simplex\ncoding and link optimization. IEEE Photonics Technol. Lett. 18(17):\n1879-1881 (2006).\n[2] M. A. Soto, et al. Raman-based distributed temperature sensor with 1 m\nspatial resolution over 26 km SMF using low-repetition-rate cyclic pulse\ncoding. Opt. Lett. 36(13): 2557-2559 (2011).\n[3] J. B. Rosolem, et al. Raman DTS based on OTDR improved by using\ngain-controlled EDFA and pre-shaped simplex code. IEEE Sens. J. 17(11):\n3346-3353 (2017).\n[4] X. Z. Sun, et al. Genetic-optimised aperiodic code for distributed optical\nfibre sensors. Nat. Commun. 11(1), 5774 (2020).\n[5] D. D. Chai, et al. Derived sequences decoding approach for long-range\ndistributed temperature sensors. IEEE Sens. J. 23(3): 2204-2210 (2022).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental setup, page 9, left column,\nparagraph 2, line 21, add “Furthermore, the measurement time of\nthe scheme proposed in this paper is mainly limited by the massive\ndata volume (with the effective number of sensing points reaching\n44,303) and the hardware accumulation processing time of the\nacquisition card, which are caused by its long sensing distance and\nhigh spatial resolution—rather than the complexity of its processing\narchitecture. The current measurement time (252 min) is constrained\nby the processing capability of the data acquisition card (acquisition\nrate: 1.0 GSa/s; storage depth: 512 Mpts). The massive data volume\n(approximately 700 k points per frame corresponding to a 70.0 km\nsensing distance) exceeds the on-board real-time processing limit. In\nthe future, high-performance acquisition cards will be upgraded to\noptimize the data processing pipeline, thereby eliminating the delay\ndeterioration caused by hardware bottlenecks.”\n2) In the section of Introduction, page 3, left column, paragraph 2,\nline 10, add “Currently, pulse coding schemes applied in Raman\ndistributed optical fiber sensing system are primarily classified into\nfive categories, which specifically include the Simplex coding\nscheme, Pre-Shaped Simplex Coding scheme, low-repetition-rate\ncyclic pulse coding scheme, Genetic-optimised aperiodic coding\nscheme, Derived Sequences coding scheme.\nSimplex coding scheme, as a linear coding technique based on\nHadamard matrix transformation, has its code length (in L bits)\ndetermining the number of detection signals required (L groups). For\ninstance, in 2006, J. Park, et al. achieved a spatial resolution of 17.0\nm, a temperature resolution of 3.0 °C, and a total of 2176 effective\nsensing points over a sensing distance of 37.0 km by utilizing this\ncoding scheme and link optimization techniques.\nLow-repetition-rate cyclic pulse coding scheme generates\nSimplex coding-based cyclic coding sequences using an\nacousto-optic modulator (AOM), enabling pulses to be injected into\nthe optical fiber periodically at a low repetition rate. For example, in\n2011, M. A. Soto, et al. combined the low-repetition-rate\nquasi-periodic cyclic pulse coding with a high-power fiber laser,\nachieving a spatial resolution of 1.0 m, a temperature resolution of\n3.0 °C, and 26,000 effective sensing points over a sensing distance\nof 26.0 km.\nPre-Shaped Simplex Coding scheme is based on simplex\ncoding technology and adopts a linearly increasing profile to adjust\npulse amplitude, compensating for the amplitude variation caused by\nEDFA to suppress the transient effect of the EDFA and improve\nsystem performance. For example, in 2017, J. B. Rosolem, et al.\nachieved a spatial resolution of 10.0 m, a temperature resolution of\n8.4 °C, and 6,200 effective sensing points over a sensing distance of\n62.0 km by using the pre-shaped Simplex coding and a\ngain-controlled erbium-doped fiber amplifier.\nGenetic-optimised aperiodic coding scheme utilizes a\ndistributed genetic algorithm (DGA) to generate a single-sequence\naperiodic code (GO-code), which is then converted into an optical\npulse sequence and injected into the optical fiber. For example, in\n2020, X. Z. Sun, et al. achieved a spatial resolution of 1.0 m, a\ntemperature resolution of 3.9 °C, and 39,000 effective sensing points\nover a sensing distance of 39.0 km based on the Genetic-optimised\naperiodic coding scheme.\nDerived Sequences coding scheme addresses the transient\neffect of EDFA through a derived sequence decoding method,\nthereby enhancing the performance of long-distance sensing. For\ninstance, in 2022, D. D. Chai, et al. achieved a spatial resolution of\n5.0 m, a temperature resolution of 2.5 °C, and 8,800 effective\nsensing points over a sensing distance of 44.0 km based on the\nDerived Sequences coding scheme.”\n4. More in-depth discussions should be provided to talk about the physical limit of\ncurrent performance and potential ways for further enhancement.\nReply: We gratefully thanks for the precious time you spent making\nconstructive remarks, we fully agree with the reviewers. In the Discussion\nsection of the revised version of this manuscript, we have added content\nregarding the physical limit of the current performance of the proposed scheme\nas well as potential approaches for further enhancement. The specific added parts\nare as follows.\nIn this proposed scheme, the physical limitations on the optimization of\nsensing distance and SNR mainly stem from two aspects: the insufficient\nperformance of experimental devices and the physical demodulation principle.\nIn terms of experimental devices, the maximum coding bit length of the\ndigital delayed pulse generator (DDPG) and the sampling rate of the data\nacquisition card are key factors restricting the improvement of the sensing\ndistance and SNR of this scheme. The CIQTEK ASG8100 model DDPG used in\nthe experiment has a maximum coding bit length of 99 bits. Since the bit length\nof Golay complementary sequences is typically 2ⁿ, a coding length of 64 bits was\nselected in the experiment. The coding length directly determines the coding gain\nof the system, which in turn affects the extent of improvement in sensing\nperformance. Therefore, it is planned to adopt a DDPG with a higher maximum\ncoding bit length (e.g., ≥128 bits) in the future to increase the system's coding\nlength, thereby achieving better sensing distance performance. In addition, the\ncurrently used data acquisition card has a sampling rate of 1.0 GSa/s and a\nmaximum number of sampling points of 700,000, corresponding to a theoretical\nmaximum sensing distance of approximately 70.0 km. Future plans involve\nupgrading to a data acquisition card with a higher sampling rate (e.g., ≥2 GSa/s)\nand a larger number of sampling points (e.g., ≥1,000,000) to eliminate the\nlimitations imposed by hardware devices on the sensing distance.\nIn terms of the physical demodulation principle, the stimulated\nscattering threshold and fiber dispersion effect also affect the improvement of\nsensing distance and SNR in this scheme. Firstly, the stimulated scattering\nthreshold of single-mode fibers is relatively low, which limits the maximum optical power\ninjected into the fiber. As a result, the intensity of the Raman backscattered\nsignal excited in the fiber is relatively weak, leading to a low SNR. In the\nfuture, we will attempt to use few-mode fibers to increase the optical power\ninjected into the fiber while minimizing intermodal dispersion as much as\npossible. Finally, fiber dispersion introduced by long-distance transmission\ncauses pulse broadening and intersymbol interference, which destroys the\northogonality of sequences. This results in the broadening of demodulated\ncorrelation peaks and a reduction in their amplitude, impairing both SNR and\ndistance resolution. This issue can be compensated for by introducing\ndispersion-compensating fibers.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Discussion, page 21, right column, paragraph 3,\nline 35, add “In this proposed scheme, the physical limitations on\nthe optimization of sensing distance and SNR mainly stem from two\naspects: the insufficient performance of experimental devices and\nthe physical demodulation principle.\nIn terms of experimental devices, the maximum coding bit\nlength of the digital delayed pulse generator (DDPG) and the\nsampling rate of the data acquisition card are key factors restricting\nthe improvement of the sensing distance and SNR of this scheme.\nThe CIQTEK ASG8100 model DDPG used in the experiment has a\nmaximum coding bit length of 99 bits. Since the bit length of Golay\ncomplementary sequences is typically 2ⁿ, a coding length of 64 bits\nwas selected in the experiment. The coding length directly\ndetermines the coding gain of the system, which in turn affects the\nextent of improvement in sensing performance. Therefore, it is\nplanned to adopt a DDPG with a higher maximum coding bit length\n(e.g., ≥128 bits) in the future to increase the system's coding length,\nthereby achieving better sensing distance performance. In addition,\nthe currently used data acquisition card has a sampling rate of 1.0\nGSa/s and a maximum number of sampling points of 700,000,\ncorresponding to a theoretical maximum sensing distance of\napproximately 70.0 km. Future plans involve upgrading to a data\nacquisition card with a higher sampling rate (e.g., ≥2 GSa/s) and a\nlarger number of sampling points (e.g., ≥1,000,000) to eliminate the\nlimitations imposed by hardware devices on the sensing distance.\nIn terms of the physical demodulation principle, the stimulated\nscattering threshold and fiber dispersion effect also affect the\nimprovement of sensing distance and SNR in this scheme. Firstly,\nthe stimulated scattering threshold of single-mode fibers is relatively\nlow, which limits the maximum optical power injected into the fiber.\nAs a result, the intensity of the Raman backscattered signal excited\nin the fiber is relatively weak, leading to a low SNR. In the future,\nwe will attempt to use few-mode fibers to increase the optical power\ninjected into the fiber while minimizing intermodal dispersion as\nmuch as possible. Finally, fiber dispersion introduced by\nlong-distance transmission causes pulse broadening and\nintersymbol interference, which destroys the orthogonality of sequences. This\nresults in the broadening of demodulated correlation peaks and a\nreduction in their amplitude, impairing both SNR and distance\nresolution. This issue can be compensated for by introducing\ndispersion-compensating fibers.”\n5. Details of Haar wavelet denoising should be provided. How is it implemented?\nDoes it sacrifice spatial resolution?\nReply: We gratefully thanks for the precious time you spent making\nconstructive remarks, we fully agree with the reviewers. In the revised\nmanuscript, we have added content regarding the implementation method of\nHaar wavelet denoising and its limitations (specifically, the impact on the spatial\nresolution of the sensing system). The specific added information is as follows.\nThe Haar wavelet function generates a set of orthogonal basis functions\nthrough translation and scaling, enabling multi-scale decomposition of signals.\nIts inherent advantage in processing low-complexity signals with abrupt change\ncharacteristics makes it particularly suitable for the analysis of Raman\nbackscattered signals.\nIn the experiment, to further improve the SNR of Raman backscattered\nsignals, we adopted a 6-level decomposition Haar wavelet. An important reason\nfor selecting the Haar wavelet is that the processed signals typically exhibit\nstep-like characteristics, which helps to retain the abrupt change structure of\nRaman backscattered signals to the greatest extent, thereby slightly mitigating\nthe impact of denoising processes using other wavelet types on the abrupt\ntemperature signals of the system.\nFurthermore, in the post-processing stage of temperature demodulation, to\nfurther suppress noise and enhance signal smoothness, we additionally applied\nthe db10 (Daubechies wavelet 10) wavelet function with 4-level decomposition.\nIt should be noted that while this step improves signal quality (by reducing\ntemperature fluctuation), it moderately degrades the spatial resolution of the\nsystem. Such parameter adjustment reflects the necessary trade-off between\nspatial resolution and temperature measurement accuracy.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental results, page 13, left column,\nparagraph 2, line 26, add “The Haar wavelet function generates a\nset of orthogonal basis functions through translation and scaling,\nenabling multi-scale decomposition of signals. Its inherent\nadvantage in processing low-complexity signals with abrupt change\ncharacteristics makes it particularly suitable for the analysis of\nRaman backscattered signals.\nIn the experiment, to further improve the SNR of Raman\nbackscattered signals, we adopted a 6-level decomposition Haar\nwavelet. Furthermore, in the post-processing stage of temperature\ndemodulation, to further suppress noise and enhance signal\nsmoothness, we additionally applied the db10 (Daubechies wavelet\n10) wavelet function with 4-level decomposition. It should be noted\nthat while this step improves signal quality (by reducing temperature\nfluctuation), it moderately degrades the spatial resolution of the\nsystem. Such parameter adjustment reflects the necessary trade-off\nbetween spatial resolution and temperature measurement accuracy.”\n6. It is confusing why the temperature-measurement uncertainty can be much larger\nthan the resolution.\nReply: We apologize for the ambiguous expression. In the revised\nmanuscript, we have supplemented two parts of content, namely the\ndefinitions of temperature fluctuation and temperature resolution as well as\ntheir respective calculation methods. The supplementary content is specified\nas follows.\n(1) Temperature fluctuation is expressed as the difference between the\nmeasured temperature and the ambient temperature. Specifically, in a Raman\ndistributed fiber optic sensing system, there exists a discrepancy between the\ndemodulated temperature (T') at the sampling points of the sensing fiber and\nthe ambient reference temperature (T₀). This discrepancy is defined as\ntemperature fluctuation (ΔT=T'－T₀). In the experiments of this manuscript,\nthe maximum temperature difference (i.e., the maximum temperature\nfluctuation) observed at the end of the 70.0 km sensing fiber was 20.86 ℃.\nTemperature resolution refers to temperature uncertainty, which\ncharacterizes the system's ability to distinguish temperature changes, is\ngenerally defined as the standard deviation (σ) of measured temperatures\nunder constant temperature conditions (e.g., a section of reference fiber) [1][2].\nIn this experiment, by calculating the standard deviation of temperatures at\nthe reference fiber, the temperature resolution at a sensing distance of 70.0\nkm was determined to be 5.39 ℃.\n(2) Theoretically, the reason why the value of temperature fluctuation is\ngreater than that of temperature resolution mainly lies in the difference in the\ntypes of errors they characterize:\nTemperature fluctuation (ΔT) primarily reflects systematic errors, which\nstem from inherent biases or calibration errors of the system (such as light\nsource power drift, deviation in the estimation of fiber link loss, errors in the\nselection of ambient temperature reference points, etc.). Such errors manifest\nas a relatively fixed offset in measurements (e.g., 20.86 ℃ in this case), and\ntheir magnitude is closely related to the sensing distance (the longer the\ndistance, the more significant the accumulation effect of systematic errors).\nMoreover, they cannot be eliminated by averaging multiple measurements.\nTemperature resolution (σ) mainly characterizes random errors or noise\nlevels (such as shot noise, thermal noise, amplifier noise, optical path noise,\netc.). It determines the minimum temperature change that the system can\nresolve. Random errors follow a statistical distribution in multiple\nmeasurements and can be suppressed to a certain extent through techniques\nsuch as signal averaging or filtering (e.g., in this case, wavelet denoising is\nemployed to improve the signal-to-noise ratio, thereby enhancing the\nresolution to 5.39 ℃).\n[1] X. Liu, et al. High-speed and high-resolution YAG fiber based distributed\nhigh temperature sensing system empowered by a 2D image restoration\nalgorithm. Opt. Express, 31(4): 6170-6183 (2023).\n[2] J. Gasser, et al. Distributed temperature sensor combining centimeter\nresolution with hundreds of meters sensing range. Opt. Express, 30(5):\n6768-6777 (2022).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental results, page 15, left column,\nparagraph 2, line 28, add “Temperature fluctuation is expressed as\nthe difference between the measured temperature and the ambient\ntemperature. Specifically, in a Raman distributed fiber optic sensing\nsystem, there exists a discrepancy between the demodulated\ntemperature (T') at the sampling points of the sensing fiber and the\nambient reference temperature (T₀). This discrepancy is defined as\ntemperature fluctuation (ΔT=T'－T₀).”\n2) In the section of Experimental results, page 16, left column,\nparagraph 3, line 29, add “Temperature resolution refers to\ntemperature uncertainty, which characterizes the system's ability to\ndistinguish temperature changes, is generally defined as the standard\ndeviation (σ) of measured temperatures under constant temperature\nconditions (e.g., a section of reference fiber) [34-35].”\n7. Some minor mistakes should be revised. For example, peak-to-peak ratio from\n0.0067 to 0.0006 should be attributed to Haar wavelet denoising instead of to\nEAC-coding. Results for the single-pulse scheme are shown in Fig.5(b1) instead of\nFig.5(b2).\nReply: We sincerely apologize for any misunderstandings caused to the\nreviewers due to some ambiguous expressions in our manuscript. We have\nrevised all the relevant content in accordance with your comments.\nIn the experiment, the improvement in the peak-to-peak ratio (from\n0.0067 to 0.0006) is jointly determined by the Haar wavelet denoising and\nthe EAC-coding scheme, as shown in Fig. 2. We applied the Haar wavelet\ndenoising algorithm to both the traditional single-pulse scheme and the\nEAC-coding scheme, with all denoising settings being completely consistent.\nFig. 2(b1) presents the Raman backscattered signals of the traditional\nsingle-pulse scheme before and after Haar wavelet denoising, where the\npeak-to-peak ratio is reduced from 0.0118 to 0.0011. Fig. 2(b2) shows the\nRaman backscattered signals of the EAC-coding scheme before and after\nHaar wavelet denoising, with the peak-to-peak ratio decreasing from 0.0067\nto 0.0006. Therefore, the combination of the EAC-coding and Haar wavelet\ndenoising scheme results in a peak-to-peak ratio of 0.0006. We have revised\nthe relevant sentences in the manuscript to avoid misunderstandings.\nFig.2. (b1) Intensity of Raman backscattered signals based on EAC-coding scheme at\nthe end of sensing fiber. (b2) Intensity of Raman backscattered signals based on\nconventional single pulse at the end of sensing fiber.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental results, page 13, left column,\nparagraph 1, line 10, add “(with Haar wavelet).”\nResponds to the reviewers’ comments:\nReviewer 3 (Comments to the Author):\nIt is well known that Distributed Anti-Stokes Raman Thermometry (aka Raman\nOTDR) is an attractive approach for distributed temperature sensing without much\ncross-sensitivity due to strain (unlike Brillouin distributed sensors). A key challenge\nfor such a Raman OTDR is its operation in the spontaneous Raman scattering regime,\nwhich severely limits the peak power that can be used thereby limiting the sensing\nrange to 20 km.\nThe use of a coded sequence of pulses is a well-established approach in Raman\nOTDR to increase the backscattered energy without losing spatial resolution.\nSpecifically, Golay encoded sequences are attractive since they use a complementary\npair of sequences that theoretically eliminates side lobes leading to excellent spatial\nresolution and low temperature uncertainty. In this work, the authors present their\nefforts on utilizing this idea to extend the measurement range to a distance of 70 km\nwhich seem impressive at first sight.\nHowever, the above manuscript is not recommended to be published in Nature\nCommunications in its current form due to the following reasons:\nReply: We gratefully thanks for the valuable time the reviewer spent\nmaking constructive remarks. These comments are all very professional and\nhelpful for revising and improving our manuscript, as well as the meaningful\nguidance to our research.\nWe have read through comments carefully and made corrections. We\nhope meet with approval. If there are still some misleading statements in the\nreply, we hope you can give us your opinions again and give us another\nopportunity to revise the manuscript. We will do our best to improve this\nwork, thanks again to the professional reviewers.\n1. There is a fundamental question on the improvement achieved in this work\ncompared to previous work. The authors claim that their work “introduces Golay\ncomplementary sequences into Raman distributed optical fiber sensing”, which is not\ntrue. In fact, it is surprising that they are not aware of previous work on this\n(10.1109/JSEN.2022.3229417) from the same University. In general, the authors need\nto present a thorough literature survey of previous work in this area and provide a\nclear justification of how their work is different from the previous approaches/results.\nReply: We would like to express our sincere gratitude to the reviewer\nfor their insightful comments. We fully concur with their suggestions and\nhave revised the manuscript accordingly to address all the points raised.\nFurthermore, we are sorry that we used some imperfect words, which caused\nambiguity about the innovation of this manuscript. The innovation of this\nmanuscript lies in proposing a novel Enhanced anti-distortion coding\n(EAC-coding) demodulation scheme that combines the autocorrelation\ncharacteristic analysis with waveform analysis and reconstruction of Raman\nbackscattered signals. This scheme is different from the conventional Golay\ncomplementary sequences. Based on the reviewer’s professional suggestions,\nwe have made revisions to this manuscript in the following three aspects:\nFirst, we have redefined the innovation of this manuscript. Second, we have\nconducted a more comprehensive investigation of the technologies in this\nfield and performed a detailed comparative analysis between the EAC-coding\nscheme and the scheme described in the reference for comparison\n(10.1109/JSEN.2022.3229417). Finally, we have compared the technical\ncharacteristics of the proposed EAC-coding scheme with those of the current\nmainstream coded pulse schemes. The detailed revision contents are as\nfollows.\n(1) We have first revised the innovative aspects of this manuscript.\nEAC-coding scheme proposed in this manuscript incorporates a novel\npreprocessing framework for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered signals. The\npreprocessing architecture for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction in this scheme can effectively suppress\nthe transient effects introduced by EDFA, thereby significantly improving the\namplitude fidelity and temporal stability of the encoded pulse sequence. This\ninnovative active reconstruction mechanism in the signal domain, which is\nbased on analyzing the waveforms of Raman backscattered signals via\nforward/inverse Fourier transforms, directly eliminates the phenomenon of\ndetection pulse distortion existing in traditional demodulation schemes. The\nscope of action of the EAC-coding scheme encompasses two key aspects:\nspecifically, one is addressing the fundamental limitation of detection signal\ndistortion through physical-layer waveform reconstruction, and the other is\nperforming correlation operations between the proposed coding sequence and\nthe reconstructed Raman signal to restore the ideal cross-correlation\ncharacteristics of Golay sequences, and achieve a theoretical gain value,\nthereby breaking through the SNR-distance trade-off limit. It achieves the\ncoordinated optimization of “waveform correction, correlation characteristic\nrestoration, signal intensity enhancement”, laying a physical layer foundation\nfor long-distance sensing.\nFurthermore, the proposed EAC-coding scheme features a\nsynergistically enhanced two-stage noise suppression mechanism,\ndemonstrating innovations in multi-level joint denoising.\nFirst, EAC-coding scheme enhances the SNR of sensing signals through\nits inherent coding gain. Based on the cross-correlation characteristics of its\nsequence design, this coding scheme provides a significant inherent gain,\nwhich compensates for signal attenuation caused by long-distance\ntransmission and effectively improves the system's baseline SNR.\nFurthermore, this mechanism not only significantly boosts optical power but\nalso leverages the irrelevance between the decoding algorithm and incoherent\nnoise to achieve preliminary suppression of transmission link losses at the\nencoding-decoding level.\nSecond, aiming at the residual noise with specific time-frequency\ndomain distribution characteristics in the decoded signal, this scheme further\nintroduces Haar wavelet transform for adaptive noise filtering. The\nmulti-resolution analysis capability of the Haar wavelet enables accurate\ncapture of the local time-frequency features of noise. By performing sparse\nrepresentation of the signal at different scales (corresponding to different\nfrequency bands) and time-domain positions, it achieves effective separation\nbetween useful signals and non-stationary noise components. While\npreserving the key details of the distributed temperature signal, this method\nefficiently eliminates residual noise, significantly enhancing the clarity of the\nsignal in the time-frequency domain and the overall measurement accuracy\nof the system.\nThis three-fold synergistic mechanism, consisting of the preprocessing\nframework compensating for EDFA fluctuation, coding gain suppressing\ntransmission losses, and wavelet transform finely removing residual noise,\nbreaks through the theoretical trade-off bottleneck between SNR and sensing\ndistance in traditional schemes. This scheme provides a novel decoding\nframework for long-distance and high-precision Raman distributed optical\nfiber sensing. Experiment results indicate that, at an ultra-long distance of\n70.0 km, this scheme can achieve a spatial resolution of 1.58 m, a\ntemperature resolution of 5.39 °C, and an effective number of sensing points\nreaching 44,303. To the best of our knowledge, the effective number of\nsensing points of EAC-coding scheme currently represents the world's\nhighest level in the field of Raman distributed optical fiber sensing.\n(2) Based on the reviewer’s professional suggestions, we have\nconducted a more comprehensive investigation and comparative analysis\nof the technologies in this field. We have carried out a detailed\ncomparison between the EAC-coding scheme proposed in the\nmanuscript and the scheme described in the reference for comparison\nfrom four dimensions: preprocessing architecture, coding gain,\ndecoding steps, and system complexity.\n① In terms of the preprocessing architecture, the proposed\nEAC-coding scheme is fundamentally different from the Derived sequences\ncoding scheme in the references for comparison (which corrects the decoding\nsequence through attenuation envelope modeling). The Derived sequences\ncoding scheme constructs decoded derived sequences that maintain good\ncross-correlation with distorted detection signals through steps including\nextracting the attenuation envelope, establishing a compensation model, and\nsolving the compensation envelope via matrix operations (as shown in Eq. (8)\n- (14) of the original paper). This technology modifies the coding sequence\n(i.e., the derived sequence), and the modified sequence maintains good\ncorrelation characteristics with the detection signals. However, the detection\nsignals remain in a distorted state essentially, and the reduction in the\nintensity of Raman backscattered signals caused by the distorted detection\nsignal is not resolved. EAC-coding scheme proposed in this paper\ninnovatively constructs an active reconstruction mechanism in the signal\ndomain. Based on the forward/inverse Fourier transform to analyze the\nwaveform of Raman backscattered signals (Eq. (5) - (10) of the manuscript),\nit directly eliminates the detection pulse distortion caused by the transient\neffect of EDFA. This method not only restores the ideal cross-correlation\ncharacteristics between the Golay complementary sequence and the detection\nsignals but also achieves the coordinated optimization of “waveform\ncorrection, correlation characteristic restoration, signal intensity\nenhancement”, laying a physical layer foundation for long-distance sensing.\n② In terms of the coding gain, the scheme proposed in the reference\nfor comparison performs encoding based on Golay complementary sequences\nand conducts correlation operations for decoding using derived sequences\ngenerated from the Golay complementary sequences. However, the detection\nsignals remain in a distorted state (as stated in the first paragraph of the left\ncolumn on Page 6 of the original paper). The EAC-coding scheme in this\nmanuscript addresses the performance degradation issue of the reference\ncaused by detection signals distortion through physical-layer waveform\nreconstruction. The reference for comparison only maintains partial\ncross-correlation through sequence modification, resulting in an actual gain\nlower than the theoretical limit of √L/2. In contrast, EAC-coding scheme\nperforms Fourier-domain analytical reconstruction on Raman backscattered\nsignals to directly eliminate transient distortion, restore the ideal\ncross-correlation characteristics of Golay sequences, and achieve a\ntheoretical gain value. Furthermore, this paper integrates Haar wavelet\ndenoising to suppress time/frequency domain coupled noise, synergistically\nimproving the SNR by 8.72 dB. Ultimately, this breaks through the SNR\nbottleneck for long-distance sensing up to 70.0 km, while the reference for\ncomparison only achieves a sensing distance of 44.0 km.\n③ In terms of the decoding principle, the breakthrough of\nEAC-coding lies in addressing the fundamental limitation of detection signal\ndistortion in the reference literature through physical-layer waveform\nreconstruction. The reference for comparison adopts derived sequences to\nperform correlation decoding with distorted detection signals (as stated in the\nfirst paragraph of the left column on Page 6 of the original paper), but fails to\ncompensate for the Raman backscattered signals attenuation caused by signal\ndistortion. This results in limited Raman backscattered signals intensity and a\nsensing distance capped at 44.0 km. In contrast, the proposed scheme\nperforms correlation operations between the Golay sequence and the\nreconstructed Raman signal (with transient distortion eliminated), thereby\nbreaking through the SNR-distance trade-off limit. Ultimately, it achieves\nultra-long-distance sensing of 70.0 km, representing a 59% sensing distance\nextension compared to the scheme in the reference for comparison.\n④ In terms of the system complexity, EAC-coding achieves an\norder-of-magnitude simplification through innovations in the algorithm\narchitecture. The reference for comparison requires implementing a sequence\nof steps (including attenuation envelope extraction, nonlinear compensation\nmodeling, and matrix inversion computation) to construct derived sequences,\nwhich significantly increases the difficulty of real-time demodulation. In\ncontrast, the proposed scheme only needs a single forward/inverse Fourier\ntransform to reconstruct the Raman backscattered signal. While ensuring\nperformance, it reduces the system complexity to a level that facilitates\nengineering deployment.\n(3) Furthermore, we have systematically compared the technical\ncharacteristics of the EAC-coding scheme proposed in this manuscript\nwith those of the current mainstream pulse coding schemes.\nCurrently, the performance comparison between conventional pulse\ncoding schemes and the EAC-coding scheme proposed in this manuscript is\npresented in Table 4.\n① In terms of coding gain, the EAC-coding scheme proposed in this\nmanuscript exhibits significant advantages in SNR improvement. The core of\nthis scheme lies in the analysis and accurate reconstruction of the waveform of\nRaman backscattered signals, which effectively compensates for the detection\nsignals distortion caused by the transient effects of the system. This\nmechanism enables EAC-coding to overcome the performance bottleneck of\ntraditional derived sequences coding schemes induced by signals distortion,\nachieving a coding gain closer to the theoretical limit. Specifically, existing\nderived sequence coding scheme construct coding sequences based on Golay\ncomplementary sequences and perform correlation decoding using their\nderived sequences. The upper limit of their theoretical coding gain is √L/2\n(where L denotes the length of the coding sequence) [1]. However, due to the\nunavoidable distortion (especially transient distortion) in actual detection\nsignals, the results of their correlation operations deteriorate, leading to a\nsignificant gap between the actually achieved coding gain and this theoretical\nvalue. In contrast, the EAC-coding scheme, through the aforementioned\nsignals analysis and reconstruction mechanism, significantly suppresses the\nimpact of transient distortion on the detection signals waveform, thereby\nenabling its coding gain to approach the theoretical upper limit of √L/2.\nBenefiting from this, the proposed system ultimately achieves temperature\nsensing capability in a long-distance Raman distributed optical fiber sensing\nsystem with a sensing distance of 70.0 km.\n② In terms of measurement time, the core advantage of the\nEAC-coding scheme stems from its extremely low decoding computational\ncomplexity. This scheme achieves signals reconstruction solely through\nFourier transform, which significantly reduces the computational cost and\ntime delay of real-time data processing, thereby effectively improving the\noverall response speed of the system. Specifically, for a Simplex code with\nlength L [2], it is necessary to inject L groups of detection signals into the\noptical fiber and collect L groups of Raman backscattered signals, with its\ntheoretical minimum acquisition time being T =L×t (where t denotes the\nacquisition time of one group of Raman backscattered curves). Although the\nGenetic-optimised aperiodic coding scheme [3] only requires injecting one\ngroup of detection signals into the optical fiber, it needs additional time to\ndesign the coding sequence based on the distributed genetic algorithm. The\nDerived sequences coding scheme requires injecting 4 groups of detection\nsignals into the optical fiber, with a theoretical acquisition time of 4t.\nHowever, in the decoding stage, it involves complex steps such as extracting\nthe attenuation envelope, establishing a compensation model, and solving the\ncompensation envelope via matrix operations, which increases the time cost\nof the decoding process. The EAC-coding scheme proposed in this\nmanuscript performs encoding based on Golay complementary sequences,\nwith a theoretical acquisition time of 4t, and only needs Fourier transform to\ncomplete the analysis and reconstruction of the Raman backscattered signals\nwaveform. This significant efficiency improvement at the algorithm level\ngreatly reduces the real-time data processing delay and effectively enhances\nthe system response speed, providing crucial real-time guarantee for the final\nrealization of temperature sensing in a 70.0 km long-distance Raman\ndistributed optical fiber sensing system.\n③ In terms of system complexity, the core innovation of the\nEAC-coding scheme lies in achieving a high degree of simplification in the\ndecoding process through algorithm optimization, while keeping the\nhardware architecture unchanged. This scheme only needs to perform\nefficient Fourier transform operations to complete signal reconstruction,\nwhich significantly reduces the algorithmic complexity and computational\nburden of real-time data processing. The specific reasons are as follows.\nSimplex coding scheme requires the injection of L groups of detection\nsignals, resulting in a long acquisition time and a large volume of raw data.\nThis not only imposes high requirements on hardware performance (such as\ndata acquisition rate and storage capacity) and long-term stability, but also\nthe large-scale data processing involved in its decoding process significantly\nincreases the computational complexity. Genetic-optimised aperiodic coding\nschemem greatly shortens the acquisition time without increasing hardware\ncosts. However, due to its unique design, it is necessary to design coding\nsequences based on a distributed genetic algorithm and conduct extensive\ntests to find the optimal coding sequence. Derived sequences coding scheme\nalso does not require additional hardware overhead. However, this scheme\nintroduces high computational complexity in the decoding stage, as it relies\non computationally expensive matrix operations to generate and process\nderived sequences.\nEAC-coding scheme proposed in this manuscript incorporates a novel\npreprocessing framework for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered signals. This\nframework significantly improves the fidelity and transmission stability of the\nencoded pulse sequence by dynamically compensating for the transient\ngain fluctuation of EDFA. This technology leverages the inherent gain of\nEAC-coding pulse coding to effectively offset fiber scattering attenuation\nduring 70.0 km long-distance transmission, achieving a significant\nimprovement in the baseline SNR. On this basis, a two-stage noise\nsuppression method is further constructed. The first-stage processing\ninvolves compensating for signal attenuation using the theoretical coding\ngain of EAC-coding. For the second-stage processing, a Haar wavelet\ndenoising algorithm is adopted. Its step-matching characteristic enables\naccurate extraction of the abrupt temperature change features of the sensing\nfiber and adaptive filtering of the residual time/frequency domain coupled\nnoise in the decoded signal. This three-fold synergistic mechanism,\nconsisting of the preprocessing framework compensating for EDFA\nfluctuation, coding gain suppressing transmission losses, and wavelet\ntransform finely removing residual noise, breaks through the theoretical\ntrade-off bottleneck between SNR and sensing distance in traditional\nschemes. Experiment results indicate that, at an ultra-long distance of 70.0\nkm, this scheme can achieve a spatial resolution of 1.58 m, a temperature\nresolution of 5.39 °C, and an effective number of sensing points reaching\n44,303, verifying the engineering feasibility of the scheme.\nTable 4. Sensing performance of various coding schemes.\n[1] D. D. Chai, et al. Derived sequences decoding approach for long-range\ndistributed temperature sensors. IEEE Sens. J. 23(3): 2204-2210 (2022).\n[2] J. Park, et al. Raman-based distributed temperature sensor with simplex\ncoding and link optimization. IEEE Photonics Technol. Lett. 18(17):\n1879-1881 (2006).\n[3] X. Z. Sun, et al. Genetic-optimised aperiodic code for distributed optical\nfibre sensors. Nat. Commun. 11(1), 5774 (2020).\n[4] M. A. Soto, et al. Raman-based distributed temperature sensor with 1 m\nspatial resolution over 26 km SMF using low-repetition-rate cyclic pulse\ncoding. Opt. Lett. 36(13): 2557-2559 (2011).\n[5] J. B. Rosolem, et al. Raman DTS based on OTDR improved by using\ngain-controlled EDFA and pre-shaped simplex code. IEEE Sens. J. 17(11):\n3346-3353 (2017).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the (unmodified manuscript) section of Experimental results,\npage 10, right column, paragraph 2, line 29, delete “Raman\ndistributed optical fiber sensing has emerged as a pivotal technology\nfor continuous temperature monitoring in long-range infrastructure\nand environmental applications. However, its practical\nimplementation over distances exceeding 30 km has been\nfundamentally hindered by the inherently low signal-to-noise ratio\n(SNR) of Raman scattering signals, which creates a critical trade-off\nbetween sensing distance and spatial resolution. In this study, we\npresent a novel Raman distributed optical fiber sensing system\nutilizing the proposed EAC-coding scheme, which effectively\nsuppresses transient effects and significantly enhances the SNR of\nsystem while incorporating Haar wavelet. This system enables\nlong-distance Raman distributed temperature measurement with\nhigh spatial resolution, achieving precise temperature demodulation\nand accurate identification of FUT position and length. The\nexperimental results demonstrate that the proposed scheme achieves\na spatial resolution of 1.58 m, temperature resolution of 5.39 ℃, and\ntemperature measurement accuracy of 0.88 ℃ at the sensing\ndistance of 70 km, establishing a new approach for long-distance\nRaman distributed optical fiber sensing system. Future research will\nintegrate more advanced denoising techniques to extend the system's\nsensing distance while preserving its spatial resolution capabilities.”\n2) In the section of Experimental results, page 18, left column,\nparagraph 2, line 10, add “EAC-coding scheme proposed in this\npaper incorporates a novel preprocessing framework for\nautocorrelation characteristic analysis, waveform analysis and\nreconstruction of Raman backscattered signals. The preprocessing\narchitecture for autocorrelation characteristic analysis, waveform\nanalysis and reconstruction in this scheme can effectively suppress\nthe transient effects introduced by EDFA, thereby significantly\nimproving the amplitude fidelity and temporal stability of the\nencoded pulse sequence. This innovative active reconstruction\nmechanism in the signal domain, which is based on analyzing the\nwaveforms of Raman backscattered signals via forward/inverse\nFourier transforms, directly eliminates the phenomenon of detection\npulse distortion existing in traditional demodulation schemes. The\nscope of action of the EAC-coding scheme encompasses two key\naspects: specifically, one is addressing the fundamental limitation of\ndetection signal distortion through physical-layer waveform\nreconstruction, and the other is performing correlation operations\nbetween the proposed coding sequence and the reconstructed Raman\nsignal to restore the ideal cross-correlation characteristics of Golay\nsequences, and achieve a theoretical gain value, thereby breaking\nthrough the SNR-distance trade-off limit. It achieves the coordinated\noptimization of “waveform correction, correlation characteristic\nrestoration, signal intensity enhancement”, laying a physical layer\nfoundation for long-distance sensing.\nFurthermore, the proposed EAC-coding scheme features a\nsynergistically enhanced two-stage noise suppression mechanism,\ndemonstrating innovations in multi-level joint denoising.\nFirst, EAC-coding scheme enhances the SNR of sensing signals\nthrough its inherent coding gain. Based on the cross-correlation\ncharacteristics of its sequence design, this coding scheme provides a\nsignificant inherent gain, which compensates for signal att\nenuation caused by long-distance transmission and effectively\nimproves the system's baseline SNR. This mechanism not only\nsignificantly boosts optical power but also leverages the irrelevance\nbetween the decoding algorithm and incoherent noise to achieve\npreliminary suppression of transmission link losses at the\nencoding-decoding level.\nSecond, aiming at the residual noise with specific\ntime-frequency domain distribution characteristics in the decoded\nsignal, this scheme further introduces Haar wavelet transform for\nadaptive noise filtering. The multi-resolution analysis capability of\nthe Haar wavelet enables accurate capture of the local\ntime-frequency features of noise. By performing sparse\nrepresentation of the signal at different scales (corresponding to\ndifferent frequency bands) and time-domain positions, it achieves\neffective separation between useful signals and non-stationary noise\ncomponents. While preserving the key details of the distributed\ntemperature signal, this method efficiently eliminates residual noise,\nsignificantly enhancing the clarity of the signal in the\ntime-frequency domain and the overall measurement accuracy of the\nsystem.\nThis three-fold synergistic mechanism, consisting of the\npreprocessing framework compensating for EDFA fluctuation,\ncoding gain suppressing transmission losses, and wavelet transform\nfinely removing residual noise, breaks through the theoretical\ntrade-off bottleneck between SNR and sensing distance in traditional\nschemes. This scheme provides a novel decoding framework for\nlong-distance and high-precision Raman distributed optical fiber\nsensing. Experiment results indicate that, at an ultra-long distance of\n70.0 km, this scheme can achieve a spatial resolution of 1.58 m, a\ntemperature resolution of 5.39 °C, and an effective number of\nsensing points reaching 44,303. To the best of our knowledge, the\neffective number of sensing points of EAC-coding scheme currently\nrepresents the world's highest level in the field of Raman distributed\noptical fiber sensing.”\n3) In the (unmodified manuscript) section of Introduction, page 3,\nleft column, paragraph 2, line 3, delete “ In this work, an\nenhanced autocorrelation pulse coding (EAC-coding) scheme is\nproposed, which introduces Golay complementary sequences into\nRaman distributed optical fiber sensing, and at the same time\nrestores the autocorrelation which is destroyed by the transient effects\nof erbium-doped fiber amplifier (EDFA) by preprocessing the Raman\nbackscattered signals for analysis and\nwaveform-reconstruction. The proposed scheme further incorporates\nHaar wavelet denoising algorithm to enhance system performance.\nIn the experiment, a Raman distributed optical fiber sensing with\nsensing distance of 70.0 km, spatial resolution of 1.58 m and\ntemperature resolution of 5.39 ℃ is achieved, which provides a new\nsolution for the research of long-distance Raman distributed optical\nfiber sensing.”\n4) In the section of Introduction, page 4, left column, paragraph 4,\nline 35, add “To address the aforementioned issues, an Enhanced\nanti-distortion coding (EAC-coding) scheme is proposed in this\npaper. This scheme effectively overcomes the trade-off dilemma\namong SNR, sensing distance, and hardware cost in traditional\nmethods through a three-fold synergistic mechanism: compensating\nfor EDFA fluctuation via a preprocessing framework, suppressing\ntransmission losses through coding gain, and finely removing\nresidual noise using wavelet transform. While maintaining relatively\nlow complexity, the EAC-coding scheme significantly enhances the\nanti-distortion capability and adaptability of the system, providing a\nnew solution for long-distance, high-performance Raman distributed\noptical fiber sensing. Experimental results demonstrate that at an\nultra-long distance of 70.0 km, the system achieves a spatial\nresolution of 1.58 m and a temperature resolution of 5.39 ℃, with\nthe number of effective sensing points reaching 44,303. To the best\nof our knowledge, this number of effective sensing points represents\nthe highest level in the field of Raman distributed optical fiber\nsensing. In addition, the preprocessing architecture within\nEAC-coding (autocorrelation characteristic analysis, waveform\nanalysis and reconstruction of Raman backscattered signals) significantly\nenhances the temporal fidelity and transmission stability of encoded\nsequences by dynamically compensating for EDFA transient gain\nfluctuation. This further improves the SNR and temperature\nmeasurement accuracy performance, enabling the temperature\nmeasurement accuracy to reach 0.91 ℃, verifying the engineering\nfeasibility of the scheme.”\n5) In the section of Discussion, page 19, right column, paragraph 4,\nline 7, add “Currently, the pulse coding techniques applied in\nRaman distributed optical fiber sensing system mainly include the\nfollowing: Simplex coding scheme, Pre-Shaped Simplex coding\nscheme, Low-repetition-rate cyclic pulse coding scheme,\nGenetic-optimised aperiodic coding scheme, and Derived Sequences\ncoding scheme. Their key performance indicators are presented in\nTable 2.\nTable 2. Sensing performance of various coding schemes.\nWe have compared our proposed scheme with other coding\nmethods such as simplex coding and Genetic-optimised aperiodic\ncoding in terms of coding gain, measurement time, and system\ncomplexity. The specific revisions are as follows.\nIn terms of coding gain, the EAC-coding scheme proposed in\nthis paper exhibits significant advantages in SNR improvement. The\ncore of this scheme lies in the analysis and accurate reconstruction\nof the waveform of Raman backscattered signals, which effectively\ncompensates for the detection signals distortion caused by the\ntransient effects of the system. This mechanism enables EAC-coding\nto overcome the performance bottleneck of traditional derived\nsequences coding schemes induced by signals distortion, achieving a\ncoding gain closer to the theoretical limit. Specifically, existing\nderived sequence coding scheme construct coding sequences based\non Golay complementary sequences and perform correlation\ndecoding using their derived sequences. The upper limit of their\ntheoretical coding gain is √L/2 (where L denotes the length of the\ncoding sequence). However, due to the unavoidable distortion\n(especially transient distortion) in actual detection signals, the\nresults of their correlation operations deteriorate, leading to a\nsignificant gap between the actually achieved coding gain and this\ntheoretical value. In contrast, the EAC-coding scheme, through the\naforementioned signals analysis and reconstruction mechanism,\nsignificantly suppresses the impact of transient distortion on the\ndetection signals waveform, thereby enabling its coding gain to\napproach the theoretical upper limit of √L/2. Benefiting from this,\nthe proposed system ultimately achieves temperature sensing\ncapability in a long-distance Raman distributed optical fiber sensing\nsystem with a sensing distance of 70.0 km.\nIn terms of measurement time, the core advantage of the\nEAC-coding scheme stems from its extremely low decoding\ncomputational complexity. This scheme achieves signals\nreconstruction solely through Fourier transform, which significantly\nreduces the computational cost and time delay of real-time data\nprocessing, thereby effectively improving the overall response speed\nof the system. Specifically, for a Simplex code with length L, it is\nnecessary to inject L groups of detection signals into the optical fiber\nand collect L groups of Raman backscattered signals, with its\ntheoretical minimum acquisition time being T =L×t (where t\nSimplex\ndenotes the acquisition time of one group of Raman backscattered\ncurves). Although the Genetic-optimised aperiodic coding scheme\nonly requires injecting one group of detection signals into the optical\nfiber, it needs additional time to design the coding sequence based\non the distributed genetic algorithm. The Derived sequences coding\nscheme requires injecting 4 groups of detection signals into the\noptical fiber, with a theoretical acquisition time of 4t. However, in\nthe decoding stage, it involves complex steps such as extracting the\nattenuation envelope, establishing a compensation model, and\nsolving the compensation envelope via matrix operations, which\nincreases the time cost of the decoding process. The EAC-coding\nscheme proposed in this paper performs encoding based on Golay\ncomplementary sequences, with a theoretical acquisition time of 4t,\nand only needs Fourier transform to complete the analysis and\nreconstruction of the Raman backscattered signals waveform. This\nsignificant efficiency improvement at the algorithm level greatly\nreduces the real-time data processing delay and effectively enhances\nthe system response speed, providing crucial real-time guarantee for\nthe final realization of temperature sensing in a 70.0 km\nlong-distance Raman distributed optical fiber sensing system.\nIn terms of system complexity, the core innovation of the\nEAC-coding scheme lies in achieving a high degree of\nsimplification in the decoding process through algorithm\noptimization, while keeping the hardware architecture unchanged.\nThis scheme only needs to perform efficient Fourier transform\noperations to complete signal reconstruction, which significantly\nreduces the algorithmic complexity and computational burden of\nreal-time data processing. The specific reasons are as follows.\nSimplex coding scheme requires the injection of L groups of detection\nsignals, resulting in a long acquisition time and a large volume of raw data.\nThis not only imposes high requirements on hardware performance\n(such as data acquisition rate and storage capacity) and long-term\nstability, but also the large-scale data processing involved in its\ndecoding process significantly increases the computational complexity.\nGenetic-optimised aperiodic coding scheme greatly shortens the\nacquisition time without increasing hardware costs. However, due to\nits unique design, it is necessary to design coding sequences based on\na distributed genetic algorithm and conduct extensive tests to find\nthe optimal coding sequence. Derived sequences coding scheme also\ndoes not require additional hardware overhead. However, this scheme\nintroduces high computational complexity in the decoding stage, as it\nrelies on computationally expensive matrix operations to generate and\nprocess derived sequences.\nEAC-coding scheme proposed in this paper incorporates a\nnovel preprocessing framework for autocorrelation characteristic\nanalysis, waveform analysis and reconstruction of Raman\nbackscattered signals. This framework significantly improves the\nfidelity and transmission stability of the encoded pulse sequence by\ndynamically compensating for the transient gain fluctuation of\nEDFA. This technology leverages the inherent gain of EAC-coding\npulse coding to effectively offset fiber scattering attenuation during\n70.0 km long-distance transmission, achieving a significant\nimprovement in the baseline SNR. On this basis, a two-stage noise\nsuppression method is further constructed. The first-stage processing\ninvolves compensating for signal attenuation using the theoretical\ncoding gain of EAC-coding. For the second-stage processing, a Haar\nwavelet denoising algorithm is adopted. Its step-matching\ncharacteristic enables accurate extraction of the abrupt temperature\nchange features of the sensing fiber and adaptive filtering of the\nresidual time/frequency domain coupled noise in the decoded signal.\nThis three-fold synergistic mechanism, consisting of the\npreprocessing framework compensating for EDFA fluctuation,\ncoding gain suppressing transmission losses, and wavelet transform\nfinely removing residual noise, breaks through the theoretical\ntrade-off bottleneck between SNR and sensing distance in traditional\nschemes. Experiment results indicate that, at an ultra-long distance of\n70.0 km, this scheme can achieve a spatial resolution of 1.58 m, a\ntemperature resolution of 5.39 °C, and an effective number of\nsensing points reaching 44,303, verifying the engineering feasibility\nof the scheme. To the best of our knowledge, the number of\neffective sensing points achieved by this scheme ranks the highest in\nthe field of Raman distributed optical fiber sensing systems.”\n2. The authors explain the process of reconstructing the Raman backscattered signals\nto eliminate transient effects in Sec. 2, but it would be better to demonstrate\nexperimental proof of their approach. The results shown in Fig. 4 are alluding to this,\nbut not very convincing.\nReply: We thank the reviewer for their valuable comments. We fully\nconcur with their assessment and have revised the manuscript to incorporate\nall of their suggestions. Based on the reviewer’s professional suggestions, we\nhave added an autocorrelation processing experiment on the detection signals\ncoupled into the sensing fiber after reconstruction, aiming to further verify\nthat it eliminates the transient effects of the system. The details of the\nnewly added experiment are as follows.\nThe primary objective of the newly added experiment is to verify that\nthe reconstructed Raman backscattered signals is equivalent to the Raman\nbackscattered signal of the undistorted detection signals.\nTaking the detection signal u as an example, its attenuation envelope\nfunction can be expressed by Eq. (1).\nf  = i f f t (\n f f t ( u\nU\n f ) \n)\n(1)\nBased on Eq. (1), the detection signal coupled into the sensing fiber\nafter reconstruction can be calculated and is given by Eq. (2).\nu  = i f f t (\nf f t\nf\n u\nf t (\n(\nf\nf )\n)\n\n)\n) (2)\nThen, we performed the same processing on the four detection signals\nand conducted autocorrelation operations on the processed detection signals.\nIf Eq. (3) is satisfied, it can be verified that their autocorrelation\ncharacteristics are restored after reconstruction, with the transient effects\neffectively suppressed.\n( u u ) ( u u ) ( w w ) ( w w ) 2 l   −    −  +  −    −  = (3)\nThe experimental results are shown in Fig. 3. Fig. 3 (c1) presents the\nautocorrelation function of the detection signals with waveform distortion\ncaused by transient effects, while Fig. 3(c2) shows the autocorrelation\nfunction of the equivalent detection signals coupled into the sensing fiber\nafter reconstruction. It can be clearly observed from Fig. 3(c2) that the\nsidelobe noise of its autocorrelation function is significantly reduced, which\nverifies that its autocorrelation characteristics are restored and the transient\neffects are effectively suppressed.\nFig.3. (c1) Autocorrelation function of the detection signals before reconstruction. (c2)\nAutocorrelation function of the detection signals after reconstruction.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental results, page 11, left column,\nchange “Fig .4” to “ Fig. 4”.\nFig. 4. Intensity of Raman backscattered signals and SNR. (a1) Intensity of\nRaman backscattered signal generated by detection signal 𝑢 before and after\npre-processing. (a2) Intensity of Raman backscattered signal generated by\ndetection signal 𝑢̅ before and after pre-processing. (a3) Intensity of Raman\nbackscattered signal generated by detection signal 𝑤 before and after\npre-processing. (a4) Intensity of Raman backscattered signal generated by\ndetection signal 𝑤̅ before and after pre-processing. (b1) Intensity of Raman\nbackscattered signals decoded by distorted detection signals before and after\npre-processing. (b2) SNR of Raman backscattered signals decoded by\ndetection signals before and after pre-processing. (c1) Autocorrelation function\nof the detection signals before pre-processing. (c2) Autocorrelation function\nof the distorted detection signals after pre-processing.\n2) In the section of Experimental results, page 12, left column,\nparagraph 2, line 3, add “We have added an autocorrelation\nprocessing experiment on the detection signals coupled into the\nsensing fiber after reconstruction, aiming to further verify that it\neliminates the transient effects of the system. The details of the\nnewly added experiment are as follows. The primary objective of the\nnewly added experiment is to verify that the reconstructed Raman\nbackscattered signals is equivalent to the Raman backscattered\nsignal of the undistorted detection signals.\nTaking the detection signal u as an example, its attenuation\nenvelope function can be expressed by Eq. (8). Thus, the detection\nsignal coupled into the sensing fiber after reconstruction can be\ncalculated and is given by Eq. (17).\nu  = i f f t (\nf f t\nf\n u\nf t (\n(\nf\nf )\n)\n\n)\n) (17)\nThen, we performed the same processing on the four detection\nsignals and conducted autocorrelation operations on the processed\ndetection signals. If Eq. (18) is satisfied, it can be verified that their\nautocorrelation characteristics are restored after reconstruction, with\nthe transient effects effectively suppressed.\n(u−u)(u−u)+(w−w)(w−w)=2l (18)\nThe experimental results are shown in Fig. 4. Fig. 4 (c1)\npresents the autocorrelation function of the detection signals with\nwaveform distortion caused by transient effects, while Fig. 4(c2)\nshows the autocorrelation function of the equivalent detection\nsignals coupled into the sensing fiber after reconstruction. It can be\nclearly observed from Fig. 4(c2) that the sidelobe noise of its\nautocorrelation function is significantly reduced, which verifies that\nits autocorrelation characteristics are restored and the transient\neffects are effectively suppressed.”\n3. The improvement claimed in Fig. 4 is with respect to RBS decoded using\n“destroyed detection” signals, but the comparison presented for the Raman OTDR\n(Figs. 5-7) is with respect to single pulse Raman OTDR. Why is that? How about\ncomparing with the uncompensated RBS?\nReply: We would like to express our sincere gratitude for the reviewer’s\nprofessional comments pointed out this issue. Based on the reviewer’s\nprofessional suggestions, we have added correlation demodulation\nexperiments corresponding to Fig. 5-7, which compare three Raman\ndistributed optical fiber sensing temperature schemes: the traditional\ndemodulation scheme, the Raman backscattered sensing scheme before\ncompensation, and the Raman backscattered sensing scheme after\ncompensation. In this study, the improvements in SNR (accompanied by\nperformance enhancements in sensing distance and temperature resolution)\nare primarily attributed to the proposed EAC-coding (for coding gain\ncompensation) and Haar wavelet denoising schemes. In contrast, the\npreprocessing architecture within EAC-coding (characterized by\nautocorrelation characteristic analysis, waveform analysis and\nreconstruction of Raman backscattered signals) serves to improve the system's\ntemperature measurement accuracy by dynamically compensating for EDFA transient\ngain fluctuation and reconstructing Raman scattered signals. The detailed\nsupplementary experiment content is as follow.\nIn this manuscript, through the synergistic demodulation mechanism of\nEAC-coding (which utilizes coding gain to compensate for attenuation)\ncombined with the refined processing of Haar wavelet denoising, the\ntheoretical trade-off bottleneck between SNR and sensing distance in\ntraditional schemes is broken through. Experimental results demonstrate that\nat an ultra-long distance of 70.0 km, the system achieves a spatial resolution\nof 1.58 m and a temperature resolution of 5.39 ℃. Moreover, the\npreprocessing architecture in EAC-coding (integrating autocorrelation\ncharacteristic analysis of Raman backscattered signals and\nwaveform analysis and reconstruction) significantly enhances the\ntemporal fidelity and transmission stability of coded pulse sequences\nby dynamically compensating for EDFA transient gain fluctuation. This\nfurther improves the system's SNR and temperature measurement accuracy,\nenabling the temperature measurement accuracy to reach 0.91 ℃.\nThe results of temperature demodulation and SNR are presented in Fig.\n4. EAC-coding, by integrating the coded pulse gain with the preprocessing\narchitecture (which incorporates autocorrelation characteristic analysis of\nRaman backscattered signals and waveform analysis and reconstruction),\neffective suppression of temperature fluctuation noise along the optical fiber\nis achieved. This optimizes the temperature fluctuation range from 300 ℃ (in\nthe traditional single-pulse scheme) to 20.86 ℃, as illustrated in Fig. 4(a1) -\n(a3). The SNR measurement results are shown in Fig. 4(b1) -\n(b3). Compared with the traditional single-pulse scheme, the SNR of the Raman\nbackscattered signal after decoding based on EAC-coding is improved by\n8.72 dB. This verifies that the EAC-coding scheme proposed in this\nmanuscript effectively enhances the SNR and the sensing distance through\ncoding gain. Furthermore, we conducted additional quantitative analysis by\nevaluating the system’s temperature resolution. Temperature resolution refers\nto the minimum distinguishable temperature range of the system It is one of\nthe core parameters for evaluating the performance of Raman distributed\noptical fiber sensing systems. The temperature resolution of the conventional\nsingle-pulse scheme is shown in Fig. 4(c1). At a sensing distance of 70.0 km,\nthe traditional single-pulse scheme achieves a temperature resolution of\n29.25 ℃. In contrast, the EAC-coding scheme proposed in this paper\noptimizes the temperature resolution to 5.39 ℃ at the same sensing distance.\nMeanwhile, we further compared the temperature measurement\naccuracy performance of the system, as shown in Fig. 4(d1) - (d3). It can be\nobserved that the transient effects not only affect the SNR, temperature\nfluctuation, and temperature resolution but also exert a significant impact on\nthe system’s temperature measurement accuracy. From Fig. 6(d1) - (d3), it\ncan be observed that as the temperature of the fiber under test (FUT) gradually\nincreases, the temperature measurement error of the distorted signal demodulation\nresults becomes increasingly large. This confirms that the influence of the\ntransient effect also intensifies with rising temperature—with the temperature\nmeasurement accuracy deteriorating to a maximum of 14.98 °C at 90 °C\n(where the demodulation result is 104.98 °C). This is because with increasing\ntemperature, the elevation of the Raman backscattered curve at the FUT\nbecomes more pronounced, while transient effects exert an increasingly\nsignificant influence on signal intensity. After the preprocessing architecture\nin the EAC-coding scheme (autocorrelation characteristic analysis, waveform\nanalysis and reconstruction of Raman backscattered signals), the temperature\ndemodulation result is 90.91 ℃, and the temperature measurement\naccuracy is 0.91 ℃, representing an improvement of approximately\n16.46 times. Therefore, the EAC-coding scheme proposed in this manuscript can\neffectively improve the system’s temperature measurement accuracy, enhancing\nthe temperature measurement accuracy of the long-distance Raman distributed\noptical fiber sensing system (with a sensing distance of 70.0 km)\nto within 1.0 ℃.\nFig.4. Experimental comparison results of temperature sensing. (a1)\nTemperature demodulation results at room temperature based on single-pulse scheme.\n(a2) Temperature demodulation results at room temperature based on distorted detection\nsignals. (a3) Temperature demodulation results at room temperature based on proposed\nEAC-coding scheme. (b1) SNR based on single-pulse scheme. (b2) SNR based on\nEAC-coding scheme (without pre-processing). (b3) SNR based on proposed\nEAC-coding scheme. (c1) Temperature resolution based on single-pulse scheme. (c2)\nTemperature resolution based on EAC-coding scheme (without pre-processing). (c3)\nTemperature resolution based on proposed EAC-coding scheme. (d1) Temperature\ndemodulation results at 50 ℃ based on EAC-coding scheme and EAC-coding\nscheme (without pre-processing). (d2) Temperature demodulation results at 70 ℃ based on\nEAC-coding scheme and EAC-coding scheme (without pre-processing). (d3)\nTemperature demodulation results at 90 ℃ based on EAC-coding scheme and\nEAC-coding scheme (without pre-processing).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental results, page 14, change “Fig. 6,\nFig. 7” to “Fig. 6”.\nFig.6. Experimental comparison results of temperature sensing. (a1)\nTemperature demodulation results at room temperature based on single-pulse\nscheme. (a2) Temperature demodulation results at room temperature based on\ndistorted detection signals. (a3) Temperature demodulation results at room\ntemperature based on proposed EAC-coding scheme. (b1) SNR based on\nsingle-pulse scheme. (b2) SNR based on EAC-coding scheme (without\npre-processing). (b3) SNR based on proposed EAC-coding scheme. (c1)\nTemperature resolution based on single-pulse scheme. (c2) Temperature\nresolution based on EAC-coding scheme (without pre-processing). (c3)\nTemperature resolution based on proposed EAC-coding scheme. (d1) Temperature\ndemodulation results at 50 ℃ based on EAC-coding scheme and EAC-coding\nscheme (without pre-processing). (d2) Temperature demodulation results at 70 ℃\nbased on EAC-coding scheme and EAC-coding scheme (without pre-processing).\n(d3) Temperature demodulation results at 90 ℃ based on EAC-coding scheme and\nEAC-coding scheme (without pre-processing).\n2) In the (unmodified manuscript) section of Experimental results,\npage 9, right column, paragraph 2, line 15, delete “The SNR\nmeasurement result after decoding is shown in Fig. 6(a). Compared\nwith the conventional single-pulse scheme, the SNR at 70.0 km of\nsensing fiber is improved by 8.75 dB based on proposed\nEAC-coding scheme, which validates the superiority of the proposed\nEAC-coding scheme in SNR improvement.\nThe temperature demodulation result is shown in Fig. 6(b).\nExperimental measurement demonstrates that the proposed\nEAC-coding scheme achieves significant suppression of temperature\nfluctuation under ambient conditions, reducing the temperature\nfluctuation from ±300 ℃ maximum in the conventional single-pulse\nscheme to ±15.84 ℃.\nFurthermore, we conduct additional quantitative analyses by\nevaluating the temperature resolution of the system.\nThe temperature resolution based on the conventional\nsingle-pulse scheme and proposed EAC-coding scheme are shown in\nFig. 7(a). At the sensing distance of 70.0 km, the conventional\nsingle-pulse scheme achieves a temperature resolution of 29.25 ℃.\nIn contrast, the proposed EAC-coding scheme demonstrates\nsignificant performance enhancement by effectively improving the\nSNR, which substantially reduces system temperature fluctuation,\nresulting in a remarkable improvement of temperature resolution to\n5.39 ℃ at the same sensing distance. Meanwhile, to validate the\nspatial resolution of the proposed EAC-coding scheme, a\n40-meter-long fiber under test is positioned at the distance of 70.0\nkm and immersed in a thermostatically controlled water bath\nmaintained at 90 ℃, while the remaining portion of the sensing fiber\nis exposed to the room temperature of 20 ℃”.\n3) In the section of Experimental results, page 15, left column,\nparagraph 2, line 5, add “The results of temperature demodulation\nand SNR are presented in Fig. 6. The temperature fluctuation of the\ntraditional single-pulse scheme can be as high as approximately\n300 ℃, as shown in Fig. 6(a1). In this paper, first, by leveraging the\nsynergistic demodulation mechanism integrating EAC-coding\n(which compensates for attenuation via coding gain) and the refined\nprocessing of Haar wavelet denoising, effective suppression of\ntemperature fluctuation noise along the optical fiber is achieved.\nThis significantly reduces the system’s temperature fluctuation to\n22.51 ℃ while improving the SNR by 7.24 dB, as shown in Fig.\n6(a2) and Fig. 6(b2). Furthermore, the preprocessing architecture\nwithin EAC-coding (autocorrelation characteristic analysis, waveform\nanalysis and reconstruction of Raman backscattered signals) further reduces the\nsystem’s temperature fluctuation to\n20.86 ℃ by dynamically compensating for EDFA transient gain\nfluctuation and reconstructing Raman scattered signals. Meanwhile,\nthe SNR is further improved by an additional 1.48 dB, as shown in\nFig. 6(a3) and Fig. 6(b3).\nCompared with the temperature resolution of 29.25 ℃ achieved\nby the traditional single-pulse scheme, the EAC-coding scheme\n(integrating coding gain with Haar wavelet denoising) improves the\nsystem’s temperature resolution to 5.82 ℃, as shown in Fig. 6(c2).\nMeanwhile, the preprocessing architecture within EAC-coding\nfurther enhances the system’s temperature resolution to 5.39 ℃ by\ndynamically compensating for EDFA transient gain fluctuation and\nreconstructing Raman scattered signals, as shown in Fig. 6(c3).\nMeanwhile, we further compared the temperature measurement\naccuracy performance of the system, as shown in Fig. 6(d1) - (d3). It\ncan be observed that the transient effects not only affect the SNR,\ntemperature fluctuation, and temperature resolution but also exert a\nsignificant impact on the system’s temperature measurement\naccuracy. It can be observed that as the temperature of the fiber\nunder test (FUT) gradually increases, the temperature measurement\nerror of the distorted signal demodulation results becomes\nincreasingly large. This confirms that the influence of the transient\neffect also intensifies with rising temperature—with the temperature\nmeasurement accuracy deteriorating to a maximum of 14.98 °C at\n90.0 °C (where the demodulation result is 104.98 °C). This is\nbecause with increasing temperature, the elevation of the Raman\nbackscattered curve at the FUT becomes more pronounced, while\ntransient effects exert an increasingly significant influence on signal\nintensity. After the preprocessing architecture in the EAC-coding\nscheme (autocorrelation characteristic analysis, waveform analysis\nand reconstruction of Raman backscattered signals), the temperature\ndemodulation result is 90.91 ℃, and the temperature measurement\naccuracy is 0.91 ℃, representing an improvement of approximately\n16.46 times. Therefore, the EAC-coding scheme proposed in this\npaper can effectively improve the system’s temperature\nmeasurement accuracy, enhancing the temperature measurement\naccuracy of the long-distance Raman distributed optical fiber\nsensing system (with a sensing distance of 70.0 km) to within\n1.0 ℃.\nThrough the synergistic demodulation mechanism of\nEAC-coding (which utilizes coding gain to compensate for\nattenuation) combined with the refined processing of Haar wavelet\ndenoising, the theoretical trade-off bottleneck between SNR and\nsensing distance in traditional schemes is broken through.\nExperimental results demonstrate that at an ultra-long distance of\n70.0 km, the system achieves a spatial resolution of 1.58 m and a\ntemperature resolution of 5.39 ℃. Moreover, the preprocessing\narchitecture in EAC-coding (integrating autocorrelation\ncharacteristic analysis of Raman backscattered signals and\nwaveform analysis and reconstruction) significantly enhances the\ntemporal fidelity and transmission stability of coded pulse sequences\nby dynamically compensating for EDFA transient gain fluctuation.\nThis further improves the system's SNR and temperature\nmeasurement accuracy, enabling the temperature measurement\naccuracy to reach 0.91 ℃. In this study, the improvements in SNR\n(accompanied by performance enhancements in sensing distance and\ntemperature resolution) are primarily attributed to the proposed\nEAC-coding (for coding gain compensation) and Haar wavelet\ndenoising schemes. In contrast, the preprocessing architecture within\nEAC-coding (characterized by autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered\nsignals) serves to improve the system's temperature measurement\naccuracy by dynamically compensating for EDFA transient gain\nfluctuation and reconstructing Raman scattered signals.”\n4. If the key contribution of this work is the compensation for transients during the\namplification process, then the comparison of results should be between the\nuncompensated case and the compensated case.\nReply: We would like to express our sincere gratitude for the reviewer’s\nprofessional comments, and we also apologize for any ambiguous language\nin our manuscript that may have caused inconvenience to the reviewer. In\nfact, in this manuscript, the improvements in SNR (accompanied by\nenhancements in sensing distance and temperature resolution performance)\nare primarily attributed to the proposed EAC-coding (coding gain) and Haar\nwavelet denoising schemes. In contrast, the preprocessing architecture of\nEAC-coding improves the system’s temperature measurement accuracy by\ndynamically compensating for EDFA transient gain fluctuation and\nreconstructing Raman scattered signals.\nBased on the reviewer’s professional suggestions, we have added\ncorrelation demodulation experiments, which compare three Raman\ndistributed optical fiber sensing temperature schemes: the traditional\ndemodulation scheme, the Raman backscattered sensing scheme before\ncompensation, and the Raman backscattered sensing scheme after\ncompensation. The experimental results are presented in Fig. 5.\nThe temperature fluctuation of the traditional single-pulse scheme can\nbe as high as approximately 300 ℃. In this manuscript, first, by leveraging\nthe synergistic demodulation mechanism integrating EAC-coding (which\ncompensates for attenuation via coding gain) and the refined processing of\nHaar wavelet denoising, effective suppression of temperature fluctuation\nnoise along the optical fiber is achieved. This significantly reduces the\nsystem’s temperature fluctuation to 22.51 ℃ while improving the SNR by\n7.24 dB. Furthermore, the preprocessing architecture within EAC-coding\n(autocorrelation characteristic analysis, waveform analysis and\nreconstruction of Raman backscattered signals) further reduces the system’s\ntemperature fluctuation to 20.86 ℃ by dynamically compensating for EDFA\ntransient gain fluctuation and reconstructing Raman scattered signals.\nMeanwhile, the SNR is further improved by an additional 1.48 dB.\nCompared with the temperature resolution of 29.25 ℃ achieved by the\ntraditional single-pulse scheme, the EAC-coding scheme (integrating coding\ngain with Haar wavelet denoising) improves the system’s temperature\nresolution to 5.82 ℃. Meanwhile, the preprocessing architecture within\nEAC-coding further enhances the system’s temperature resolution to 5.39 ℃\nby dynamically compensating for EDFA transient gain fluctuation and\nreconstructing Raman scattered signals.\nMeanwhile, we further compared the temperature measurement\naccuracy performance of the system, as shown in Fig. 4(d1) - (d3). It can be\nobserved that the transient effects not only affect the SNR, temperature\nfluctuation, and temperature resolution but also exert a significant impact on\nthe system’s temperature measurement accuracy. It can be observed that as\nthe temperature of the fiber under test (FUT) gradually increases, the\ntemperature measurement error of the distorted signal demodulation results\nbecomes increasingly large. This confirms that the influence of the\ntransient effect also intensifies with rising temperature—with the temperature\nmeasurement accuracy deteriorating to a maximum of 14.98 °C at 90.0 °C\n(where the demodulation result is 104.98 °C). This is because with increasing\ntemperature, the elevation of the Raman backscattered curve at the FUT\nbecomes more pronounced, while transient effects exert an increasingly\nsignificant influence on signal intensity. After the preprocessing architecture\nin the EAC-coding scheme (autocorrelation characteristic analysis, waveform\nanalysis and reconstruction of Raman backscattered signals), the temperature\ndemodulation result is 90.91 ℃, and the temperature measurement accuracy\nis 0.91 ℃, representing an improvement of approximately 16.46 times.\nTherefore, the EAC-coding scheme proposed in this manuscript can\neffectively improve the system’s temperature measurement accuracy,\nenhancing the temperature measurement accuracy of the long-distance\nRaman distributed optical fiber sensing system (with a sensing distance of\n70.0 km) to within 1.0 ℃.\nIn conclusion, the innovation of this manuscript lies in two aspects. First,\nby leveraging the synergistic demodulation mechanism integrating\nEAC-coding (which compensates for attenuation via coding gain) and the\nrefined processing of Haar wavelet denoising, this manuscript breaks through\nthe theoretical trade-off bottleneck between SNR and sensing distance in\ntraditional schemes. Experimental results demonstrate that at an ultra-long\ndistance of 70.0 km, the system achieves a spatial resolution of 1.58 m and a\ntemperature resolution of 5.39 ℃, with the number of effective sensing\npoints reaching 44,303. To the best of our knowledge, this number of\neffective sensing points represents the highest level in the field of Raman\ndistributed optical fiber sensing. Second, the preprocessing architecture\nwithin EAC-coding (autocorrelation characteristic analysis, waveform\nanalysis and reconstruction of Raman backscattered signals) significantly\nenhances the temporal fidelity and transmission stability of encoded\nsequences by dynamically compensating for EDFA transient gain fluctuation.\nThis further improves the system’s SNR and temperature measurement\naccuracy, enabling the temperature measurement accuracy to reach 0.91 ℃.\nFig.5. Experimental comparison results of temperature sensing. (a1)\nTemperature demodulation results at room temperature based on single-pulse scheme.\n(a2) Temperature demodulation results at room temperature based on distorted detection\nsignals. (a3) Temperature demodulation results at room temperature based on proposed\nEAC-coding scheme. (b1) SNR based on single-pulse scheme. (b2) SNR based on\nEAC-coding scheme (without pre-processing). (b3) SNR based on proposed\nEAC-coding scheme. (c1) Temperature resolution based on single-pulse scheme. (c2)\nTemperature resolution based on EAC-coding scheme (without pre-processing). (c3)\nTemperature resolution based on proposed EAC-coding scheme. (d1) Temperature\ndemodulation results at 50 ℃ based on EAC-coding scheme and EAC-coding\nscheme (without pre-processing). (d2) Temperature demodulation results at 70 ℃ based on\nEAC-coding scheme and EAC-coding scheme (without pre-processing). (d3)\nTemperature demodulation results at 90 ℃ based on EAC-coding scheme and\nEAC-coding scheme (without pre-processing).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental results, page 15, left column,\nparagraph 2, line 5, add “The results of temperature demodulation\nand SNR are presented in Fig. 6. The temperature fluctuation of the\ntraditional single-pulse scheme can be as high as approximately\n300 ℃, as shown in Fig. 6(a1). In this paper, first, by leveraging the\nsynergistic demodulation mechanism integrating EAC-coding\n(which compensates for attenuation via coding gain) and the refined\nprocessing of Haar wavelet denoising, effective suppression of\ntemperature fluctuation noise along the optical fiber is achieved.\nThis significantly reduces the system’s temperature fluctuation to\n22.51 ℃ while improving the SNR by 7.24 dB, as shown in Fig.\n6(a2) and Fig. 6(b2). Furthermore, the preprocessing architecture\nwithin EAC-coding (autocorrelation characteristic analysis, waveform\nanalysis and reconstruction of Raman backscattered signals) further reduces the\nsystem’s temperature fluctuation to\n20.86 ℃ by dynamically compensating for EDFA transient gain\nfluctuation and reconstructing Raman scattered signals. Meanwhile,\nthe SNR is further improved by an additional 1.48 dB, as shown in\nFig. 6(a3) and Fig. 6(b3).\nCompared with the temperature resolution of 29.25 ℃ achieved\nby the traditional single-pulse scheme, the EAC-coding scheme\n(integrating coding gain with Haar wavelet denoising) improves the\nsystem’s temperature resolution to 5.82 ℃, as shown in Fig. 6(c2).\nMeanwhile, the preprocessing architecture within EAC-coding\nfurther enhances the system’s temperature resolution to 5.39 ℃ by\ndynamically compensating for EDFA transient gain fluctuation and\nreconstructing Raman scattered signals, as shown in Fig. 6(c3).\nMeanwhile, we further compared the temperature measurement\naccuracy performance of the system, as shown in Fig. 6(d1) - (d3). It\ncan be observed that the transient effects not only affect the SNR,\ntemperature fluctuation, and temperature resolution but also exert a\nsignificant impact on the system’s temperature measurement\naccuracy. It can be observed that as the temperature of the fiber\nunder test (FUT) gradually increases, the temperature measurement\nerror of the distorted signal demodulation results becomes\nincreasingly large. This confirms that the influence of the transient\neffect also intensifies with rising temperature—with the temperature\nmeasurement accuracy deteriorating to a maximum of 14.98 °C at\n90.0 °C (where the demodulation result is 104.98 °C). This is\nbecause with increasing temperature, the elevation of the Raman\nbackscattered curve at the FUT becomes more pronounced, while\ntransient effects exert an increasingly significant influence on signal\nintensity. After the preprocessing architecture in the EAC-coding\nscheme (autocorrelation characteristic analysis, waveform analysis\nand reconstruction of Raman backscattered signals), the temperature\ndemodulation result is 90.91 ℃, and the temperature measurement\naccuracy is 0.91 ℃, representing an improvement of approximately\n16.46 times. Therefore, the EAC-coding scheme proposed in this\npaper can effectively improve the system’s temperature\nmeasurement accuracy, enhancing the temperature measurement\naccuracy of the long-distance Raman distributed optical fiber\nsensing system (with a sensing distance of 70.0 km) to within\n1.0 ℃.\nThrough the synergistic demodulation mechanism of\nEAC-coding (which utilizes coding gain to compensate for\nattenuation) combined with the refined processing of Haar wavelet\ndenoising, the theoretical trade-off bottleneck between SNR and\nsensing distance in traditional schemes is broken through.\nExperimental results demonstrate that at an ultra-long distance of\n70.0 km, the system achieves a spatial resolution of 1.58 m and a\ntemperature resolution of 5.39 ℃. Moreover, the preprocessing\narchitecture in EAC-coding (integrating autocorrelation\ncharacteristic analysis of Raman backscattered signals and\nwaveform analysis and reconstruction) significantly enhances the\ntemporal fidelity and transmission stability of coded pulse sequences\nby dynamically compensating for EDFA transient gain fluctuation.\nThis further improves the system's SNR and temperature\nmeasurement accuracy, enabling the temperature measurement\naccuracy to reach 0.91 ℃. In this study, the improvements in SNR\n(accompanied by performance enhancements in sensing distance and\ntemperature resolution) are primarily attributed to the proposed\nEAC-coding (for coding gain compensation) and Haar wavelet\ndenoising schemes. In contrast, the preprocessing architecture within\nEAC-coding (characterized by autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered\nsignals) serves to improve the system's temperature measurement\naccuracy by dynamically compensating for EDFA transient gain\nfluctuation and reconstructing Raman scattered signals.”\n5. What do the authors mean by “destroyed detection” signals? Needs to be explained\nproperly.\nReply: We sincerely apologize for the inappropriate terminology used in this\nmanuscript. In the manuscript, the phrase “destroyed detection signals” refers to\ndetection signals whose autocorrelation characteristics have been impaired by\ntransient effects—specifically, detection signals with waveform distortion caused\nby transient effects, which correspond to the red curves 𝑢(𝑓)、𝑢̅(𝑓)、𝑤(𝑓)、\n𝑤̅(𝑓) in Fig. 3(a1) - (a4) of the manuscript. For the sake of clarity, we have\nreplaced all instances of the phrase \"destroyed detection signals\" with \"distorted\ndetection signals\" in both the main text and figure captions of the manuscript.\nAdditionally, we have supplemented the original text with a glossary explanation\nof this signal (i.e., “distorted detection signals”).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Principles and methods, page 5, change “Fig. 1”\nto “Fig. 1”.\nFig. 1. Physics principle of proposed EAC-coding scheme for Raman\ndistributed optical fiber sensing. (a) Principle of encoding based on Golay\ncomplementary sequences. (b) The influence of transient effects on Raman\nbackscattered signals. (c) RBSs generated by four distorted detection signals in\nsensing fiber; (d) Principle of decoding after analysis and\nwaveform-reconstruction based on proposed EAC-coding scheme. (e)\nTemperature demodulation principle.\n2) In the section of Principles and methods, page 5, left column,\nparagraph 3, line 18, change “destroyed detection signals” to\n“distorted detection signals”.\n3) In the section of Experimental results, page 11, right column,\nparagraph 2, line 20, change “destroyed detection signals” to\n“distorted detection signals”.\n4) In the section of Experimental results, page 11, right column,\nparagraph 2, line 27, change “destroyed detection signals” to\n“distorted detection signals”.\n6. In Fig. 6(a), the EAC scheme is shown to provide 8.75 dB improvement over the\nsingle pulse scheme. How is this 8.75 dB explained? For a 64 bit code, we expect an\nSNR improvement of sqrt(64)/2 = 4, which is 6 dB.\nReply: We would like to express our sincere gratitude for your\nprofessional comments and also thank you for pointing out this issue. The\nmaximum input optical power of the sensing fiber also affects the\nimprovement of the theory SNR of its coding scheme. We are very sorry that\nsome of the vague language in the manuscript overlooked this point, and we\nhave added these contents in the revised manuscript. In this manuscript,\nbased on the maximum optical power (0.2 mW) that can be achieved in\nconventional single-pulse demodulation scheme, the theoretical SNR of\n64-bit code demodulation scheme is improved to 6 dB under this power\ncondition. The EAC demodulation scheme proposed can enhance the\nstimulated Raman scattering (SRS) threshold of sensing fibers, enabling a\nsignificant increase in optical power input to the sensing fibers, reaching up\nto 0.7 mW. At this power level, the theoretical SNR of EAC encoding and\ndemodulation is improved to 11.46 dB. In actual experiment, since the EDFA\nintroduces a significant amount of amplified spontaneous emission (ASE)\nnoise while amplifying the effective signal, the final experimental\nimprovement in SNR is 8.72 dB, which is lower than the theoretical value of\n11.46 dB. We have also revised this section in the updated manuscript. The\nspecific reasons are as follows.\nThe establishment of the theoretical pulse gain is based on the strict\npremise that the input powers of the single-pulse demodulation scheme and\nthe pulse coding scheme are identical. In the experimental scheme of this\npaper, the input power is set to be close to the maximum value of the\nstimulated Raman scattering nonlinear effect threshold of the sensing fiber.\nFor the coding technology with a code length of 64 bits (i.e., the\nEAC-coding scheme adopted in this manuscript). Under the maximum input\npower achievable by a single pulse demodulation system (0.2 mW), the\ntheoretical SNR improvement is 6 dB.\nHowever, the theoretical 6 dB SNR improvement is based on the strict\npremise that the input powers of the single-pulse demodulation scheme and\nthe pulse coding scheme are the same. In this experiment, to explore the\nextreme performance of the EAC-coding scheme and maximize the system\nSNR, we set the input power to be close to the maximum value of the SRS\nnonlinear effect threshold of the sensing fiber. Specifically, the average\npower input into the optical fiber is approximately 0.7 mW, and the\ncalculated peak power is close to 1.4 W.\nIn contrast, the traditional single-pulse demodulation scheme, due to its\nhigher peak power (under the same average power), is more likely to trigger\nthe SRS nonlinear effect, leading to signal distortion and performance\ndegradation. Therefore, to ensure the stable operation of the single-pulse\nscheme below the nonlinear threshold, its average input power must be\nsignificantly reduced, which is set to approximately 0.2 mW in the\nexperiment.\nThe different incident powers of the two schemes are incorporated into\nthe calculation of the theoretical SNR improvement. According to Eq. (4) in\nthe manuscript, with all other factors remaining completely unchanged, the\nintensity of the Raman backscattered signal depends solely on the incident\noptical power. Thus, the modified theoretical SNR improvement is\napproximately 10log [(√64/2)×(0.7/0.2)]=11.46 dB. Meanwhile, since the\n(ASE) noise while amplifying the effective signal, the final experimental\nimprovement in SNR is 8.72 dB, which is slightly lower than the theoretical\nvalue of 11.46 dB.\nIn summary, it is precisely because the EAC-coding scheme allows a\nhigher average input power without triggering significant nonlinear effects,\nand combined with its inherent theoretical coding gain, the SNR\nimprovement observed in the experiment finally reaches 8.72 dB, which is\nslightly lower than the theoretical SNR coefficient (11.46 dB) at this power\nsetting (0.7 mW).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Discussion, page 22, right column, paragraph 3,\nline 18, add “For the coding technology with a code length of 64\nbits (i.e., the EAC-coding scheme adopted in this paper). Under the\nmaximum input power achievable by a single pulse demodulation\nsystem (0.2 mW), the theoretical SNR improvement is 6 dB.\nHowever, the theoretical 6 dB SNR improvement is based on\nthe strict premise that the input powers of the single-pulse\ndemodulation scheme and the pulse coding scheme are the same. In\nthis experiment, to explore the extreme performance of the\nEAC-coding scheme and maximize the system SNR, we set the\ninput power to be close to the maximum value of the stimulated\nRaman scattering (SRS) nonlinear effect threshold of the sensing\nfiber. Specifically, the average power input into the optical fiber is\napproximately 0.7 mW, and the calculated peak power is close to 1.4\nW.\nIn contrast, the traditional single-pulse demodulation scheme,\ndue to its higher peak power (under the same average power), is\nmore likely to trigger the SRS nonlinear effect, leading to signal\ndistortion and performance degradation. Therefore, to ensure the\nstable operation of the single-pulse scheme below the nonlinear\nthreshold, its average input power must be significantly reduced,\nwhich is set to approximately 0.2 mW in the experiment.\nThe different incident powers of the two schemes are\nincorporated into the calculation of the theoretical SNR\nimprovement. According to Eq. (4) in the paper, with all other\nfactors remaining completely unchanged, the intensity of the Raman\nbackscattered signal depends solely on the incident optical power.\nThus, the modified theoretical SNR improvement is approximately\n10log [(√64/2)×(0.7/0.2)]=11.46 dB. Since the EDFA introduces\n10\na significant amount of amplified spontaneous emission (ASE) noise\nwhile amplifying the effective signal, the final experimental\nimprovement in SNR is 8.72 dB, which is slightly lower than the\ntheoretical value of 11.46 dB.\nIn summary, it is precisely because the EAC-coding scheme\nallows a higher average input power without triggering significant\nnonlinear effects, and combined with its inherent theoretical coding\ngain, the SNR improvement observed in the experiment finally\nreaches 8.72 dB, which is slightly lower than the theoretical SNR\ncoefficient (11.46 dB) at this power setting (0.7 mW).”\n7. Also, if we check the difference between the two curves at 28 km, the improvement\nseems to be more than 10 dB. How can you explain this?\nReply: We would like to express our gratitude to the reviewer for the\nvaluable comments and in-depth corrections on this issue. In the experiment,\nwithin a range from the starting end of the sensing fiber to 56.0 km, the SNR\nimprovement of the sensing signal is about 10.44 dB; while in the region\nbeyond approximately 70.0 km at the tail end of the optical fiber, the SNR\nimprovement is 8.72 dB. The improvement of SNR at each sensing distance\npoint is lower than the theoretical value of 11.46 dB. The improvement of\nSNR at the end of sensing fiber is also lower than that at the front end of\nsensing fiber. This discrepancy primarily stems from the synergistic effect\nbetween the difference in SNR improvement between experiments and\ntheory conditions, and the distance-dependent characteristics of fiber\nattenuation. The specific theoretical analysis is as follows.\nAfter revising the SNR calculation formula, the overall SNR\nimprovement along the optical fiber obtained from the experimental results is\nslightly lower than the theoretical SNR. Since the maximum input optical\npower of the sensing fiber affects the theoretical SNR improvement of its\ncoding scheme, the final SNR magnitude calculated for the EAC-coding\nscheme is 11.46 dB. Meanwhile, due to the introduction of the EDFA, a large\namount of amplified spontaneous emission (ASE) noise is introduced during\nthe process of amplifying the detection signal—this results SNR\nimprovement in the experiment being slightly lower than the theoretical\nvalue of 11.46 dB. Consequently, the SNR improvement along the optical\nfiber derived from the experimental results (with a maximum of 10.44 dB) is\nslightly lower overall than the theoretical SNR (11.46 dB).\nFurthermore, fiber attenuation exhibits a cumulative effect with\ntransmission distance. At 70.0 km, the single-pulse signal is already close to\nthe system’s detection limit due to severe attenuation, making it difficult to\nextract effectively. Although the EAC-coding scheme still maintains a certain\nsignal advantage, the intensity difference between the EAC-coding signal and\nthe single-pulse signal is smaller than that at 28.0 km, as the signal amplitude\ndecreases significantly after long-distance transmission. Consequently, the\nSNR improvement at this location decreases to 8.72 dB. This result clearly\nreflects the distance-dependent characteristic of fiber signal attenuation and\nalso highlights the performance difference of the coding scheme at different\ntransmission distances.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Discussion, page 15, right column, paragraph 2,\nline 5, add “In the experiment, within a range from the starting end\nof the sensing fiber to 56.0 km, the SNR improvement of the sensing\nsignal is about 10.44 dB; while in the region beyond approximately\n70.0 km at the tail end of the optical fiber, the SNR improvement is\n8.72 dB. The improvement of SNR at each sensing distance point is\nlower than the theoretical value of 11.46 dB. The improvement of\nSNR at the end of sensing fiber is also lower than that at the front\nend of sensing fiber. This discrepancy primarily stems from the\nsynergistic effect between the difference in SNR improvement\nbetween experiments and theory conditions, and the\ndistance-dependent characteristics of fiber attenuation.\nAfter revising the SNR calculation formula, the overall SNR\nimprovement along the optical fiber obtained from the experimental\nresults is slightly lower than the theoretical SNR. Since the\nmaximum input optical power of the sensing fiber affects the\ntheoretical SNR improvement of its coding scheme, the final SNR\nmagnitude calculated for the EAC-coding scheme is 11.46 dB.\nMeanwhile, due to the introduction of the EDFA, a large amount of\namplified spontaneous emission (ASE) noise is introduced during\nthe process of amplifying the detection signal—this results SNR\nimprovement in the experiment being slightly lower than the\ntheoretical value of 11.46 dB. Consequently, the SNR improvement\nalong the optical fiber derived from the experimental results (with a\nmaximum of 10.44 dB) is slightly lower overall than the theoretical\nSNR (11.46 dB).\nFurthermore, fiber attenuation exhibits a cumulative effect with\ntransmission distance. At 70.0 km, the single-pulse signal is already\nclose to the system’s detection limit due to severe attenuation,\nmaking it difficult to extract effectively. Although the EAC-coding\nscheme still maintains a certain signal advantage, the intensity\ndifference between the EAC-coding signal and the single-pulse\nsignal is smaller than that at 28.0 km, as the signal amplitude\ndecreases significantly after long-distance transmission.\nConsequently, the SNR improvement at this location decreases to\n8.72 dB. This result clearly reflects the distance-dependent\ncharacteristic of fiber signal attenuation and also highlights the\nperformance difference of the coding scheme at different\ntransmission distances.”\n8. What is being plotted in Fig. 7(a)? Absolute temperature or uncertainty in\ntemperature? I presume it is the latter, in which case it should be clearly mentioned.\nHow is 6x improvement achieved? Need proper explanation?\nReply: We wish to express our sincere agreement with the reviewers'\ninsightful comments, the Fig. 7(a) (figure number of the manuscript before\nrevision) depicts the temperature uncertainty, which is used to define the\ntemperature resolution. Temperature resolution is defined as the minimum\ntemperature change that a system can reliably distinguish, and it is one of the\nkey parameters for evaluating Raman distributed optical fiber sensing\nsystems.\nIn Raman distributed optical fiber sensing, the standard calculation\nmethod for temperature resolution is based on the statistical fluctuation of\ntemperature demodulation results under steady-state conditions. Specifically,\nit is characterized and calculated by the standard deviation of temperature\ndemodulation values within a specific length under a constant temperature\nenvironment [1][2].\nThe proposed scheme compares the temperature resolution performance\nbetween the traditional single-pulse demodulation scheme and the proposed\nEAC-coding scheme. In this experiment, temperature resolution is\ncharacterized by the temperature standard deviation of each distributed\ntemperature measurement point within a fixed length of the sensing fiber.\nExperimental results show that at a sensing distance of 70.0 km, the\ntemperature resolution of the EAC-coding scheme is significantly improved\ncompared with that of the single-pulse scheme: the temperature resolution is\nenhanced from 29.25 °C (of the single-pulse scheme) to 5.39 °C,\nrepresenting an improvement of up to 5.43 times.\n[1] X. Liu, et al. High-speed and high-resolution YAG fiber based distributed\nhigh temperature sensing system empowered by a 2D image restoration\nalgorithm. Opt. Express, 31(4): 6170-6183 (2023).\n[2] J. Gasser, et al. Distributed temperature sensor combining centimeter\nresolution with hundreds of meters sensing range. Opt. Express, 30(5):\n6768-6777 (2022).\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Experimental results, page 16, left column,\nparagraph 3, line 37, add “In this experiment, temperature\nresolution is characterized by the temperature standard deviation of\neach distributed temperature measurement point within a fixed\nlength of the sensing fiber. Experimental results show that at a\nsensing distance of 70.0 km, the temperature resolution of the\nEAC-coding scheme is significantly improved compared with that of\nthe single-pulse scheme: the temperature resolution is enhanced\nfrom 29.25 °C (of the single-pulse scheme) to 5.39 °C, representing\nan improvement of up to 5.43 times.”\nCorrections:\nWe would like to express our heartfelt thanks to all reviewers for the careful\nreview of our manuscript and your valuable comments amid your busy schedules. The\nprofessional suggestions you provided have offered important guidance for improving\nthe quality of the manuscript, and we would like to extend our sincere gratitude for this.\nTo clearly present the full picture of revisions to the manuscript and facilitate the\nreviewers' verification of the implementation of these revisions, we have summarized\nall the revisions and supplements made based on the reviewers' comments.\nOnce again, we appreciate the attentive guidance from all reviewers. Should you\nhave any details requiring further communication or additional suggestions for\nimprovement during subsequent verification, we will respond promptly and fully\ncooperate, and continue to polish the manuscript with the most rigorous attitude to\nensure it meets the high standards for publication in the journal.\nThank you for your suggestion. We have made the following modifications in\nour revised manuscript:\n1) In the section of Experimental results, page 17, right column, paragraph 2,\nline 11, add “In the proposed scheme, the pulse width of a single code element is\nset to 10 ns, corresponding to a theoretical spatial resolution of 1.0 m.\nFurthermore, single-mode fiber is employed to avoid the degradation of spatial\nresolution caused by intermodal dispersion in the sensing fiber. However, the\nintensity of Raman scattering signals excited in single-mode fiber is relatively\nlow. Therefore, in the experiment, to further improve the SNR of the sensing\nsignals, Haar wavelet denoising processing is applied to the Raman anti-Stokes\nscattering signals after the decoding process. It is suitable for processing\nlow-complexity signals with mutation characteristics, thus making it well-suited\nfor handling fiber optic Raman scattering signals. Meanwhile, in this paper, after\ntemperature demodulation, the db10 wavelet method is synchronously applied to\nthe distributed temperature demodulation curve to further improve the SNR of the\nsensing signal. However, this denoising method will filter out the edge\ninformation of the temperature envelope in the sensing fiber region, resulting in a\nfinal experimentally measured spatial resolution of 1.58 m, which differs from the\ntheoretical spatial resolution of 1.0 m.”\n2) In the section of Experimental setup, page 9, right column, paragraph 2, line\n4, add “In the experimental process of this scheme, only the Raman anti-Stokes\nscattering signals were analyzed and processed, and the subsequent temperature\ndemodulation was also performed solely based on the Raman anti-Stokes\nscattering signals. Compared with the dual-path demodulation scheme (where\nRaman Stokes scattering light is used to demodulate Raman anti-Stokes\nscattering signals), this scheme has the following two specific advantages. The\nRaman anti-Stokes scattering signal based on single-path demodulation exhibits\nhigher sensitivity to the temperature distribution along the sensing fiber; The\nsingle-path demodulation scheme can enhance the system's measurement rate and\nreduce system costs.”\n3) In the section of Experimental setup, page 8, right column, paragraph 2, line\n5, add “The equipment used in the experiment, along with their corresponding\nmodel numbers, manufacturers, and key optical parameters, are listed as follows:\nLaser (KEYANG PHOTONICS; DFB Continuous laser; Center\nWavelength:1550 nm);SOA (OPEAK; OAM-SOA-PL-15-15-S; Operating\nWavelength: 1520-1570 nm); DDPG (CIQTEK; ASG8100; Maximum Coding bit:\n99 bit); EDFA (OPEAK; EDFA-C-PL-MB-100-S; Operating Wavelength: 1550\nnm); WDM (OPEAK; WDM-1*3-1550; Isolation: ≥60 dB); APD (KEYANG\nPHOTONICS; KY-DTS-200M; Bandwidth:200 MHz); DAC (CIQTEK;\nDAQ2100; Sampling Rate: 1 GSa/s). And all experimental equipment used in this\nexperiment are conventional commercial products available on the market.”\n4) In the section of Experimental results, page 12, right column, change “Fig. 5”\nto “Fig. 5”\nFig. 5. Intensity of Raman backscattered signals based on EAC-coding scheme and\nconventional single-pulse. (a) Intensity of Raman backscattered signals based on\nEAC-coding scheme and conventional single-pulse with and without Haar wavelet. (b1)\nIntensity of Raman backscattered signals based on conventional single-pulse at the end of\nsensing fiber. (b2) Intensity of Raman backscattered signals based on EAC-coding scheme at\nthe end of sensing fiber. (c1) SNR of Raman backscattered signals based on conventional\nsingle-pulse scheme at the end of sensing fiber. (c2) SNR of Raman backscattered signals\nbased on EAC-coding scheme at the end of sensing fiber.\n5) In the section of Experimental results, page 13, right column, paragraph 2,\nline 11, add “As shown in Fig. 5(c1) and 5(c2), the Haar wavelet function\nsignificantly improves the SNR for both the EAC-coding scheme proposed in this\npaper and the traditional single-pulse demodulation scheme. Experimental results\nindicate that after Haar wavelet denoising, the SNR of the EAC-coding scheme\nand the traditional single-pulse demodulation scheme is increased by 7.63 dB and\n2.92 dB, respectively. It is worth noting that a relatively significant difference\nemerges between the two demodulation schemes at the end of the sensing fiber.\nFor single-pulse scheme, the effective Raman scattering signal is basically\nsubmerged by system noise beyond 42.0 km. After incorporating the Haar\nwavelet function, although the noise level is reduced, the signal is still submerged\nby noise beyond 56.0 km. Therefore, the improvement in SNR at the end of the\nsensing fiber is relatively limited for the single-pulse scheme. This also confirms\nthat the wavelet denoising algorithm has a limited capability to improve SNR in\nlong-distance distributed optical fiber sensing demodulation schemes. Hence, we\ncombine the EAC-coding scheme with Haar wavelet denoising. Only by avoiding\nthe effective Raman scattering signal being submerged by system noise as much\nas possible can the wavelet denoising algorithm maximize the SNR of the sensing\nsignal.”\n6) In the (unmodified manuscript) section of Introduction, page 2, left column,\nparagraph 3, line 35, delete “The pulse coding scheme employs specific\nfunctional equations to encode detection signals, and then decodes the collected\nRaman backscattered signals through a decoding program [21-22]. It increases the\nintensity of the detection signals without the stimulated Raman generating\nnonlinear effects and thus improve the SNR of system. For example, Sun et al.\nproposed a genetic-optimised aperiodic coding scheme achieving a sensing\nspatial resolution of 1.0 m at the sensing distance of 39.0 km [23]. With the\ndevelopment of digital signal processing, various denoising schemes are used in\nRaman distributed optical fiber sensing, including wavelet denoising algorithm\nand dynamic sampling-correction method [24-25]. For example, M. Yu, et al.\nproposed a dynamic sampling-correction scheme achieving a sensing distance of\n20.0 km [26]. H. S. Pradhan, et al. proposed a Fourier wavelet regularised\ndeconvolution scheme achieving a sensing distance of 30.0 km with a spatial\nresolution of 3.0 m [27].\nFurthermore, the neural network scheme can learn the characteristic patterns\nof Raman scattering signals, perform convolutional operations and subsequent\nprocessing on the input signals to effectively identify and remove noise\ncomponents, thereby improving the SNR [28]. For example, Zhang et al. proposed\na deep 1-D denoising convolutional neural network scheme, which realized a\nsensing distance of 10 km with a spatial resolution of 3 m [29].\nHowever, in large-scale engineering infrastructures, fiber deployment\ntypically adopts U-shaped or Hilbert-curve configurations, necessitating length of\nsensing fiber several times infrastructures. Despite employing advanced\ndenoising schemes in Raman distributed fiber sensing [30-32], achieving a further\nbreakthrough in sensing distance remains challenging under meter-scale spatial\nresolution constraints.”\n7) In the section of Introduction, page 2, right column, paragraph 4, line 34, add\n“Pulse coding schemes have demonstrated significant advantages in\nlong-distance Raman distributed optical fiber sensing system. On one hand, by\nencoding the detection optical pulses, this technology can significantly increase\nthe optical power injected into the sensing fiber while avoiding fiber nonlinear\neffects, thereby enhancing the intensity of effective sensing signals at the level of\nsignal generation mechanism. On the other hand, at the data processing level, it\nleverages the separability between coded signals and uncoded noise to effectively\nsuppress noise and improve the SNR of system.\nCurrently, pulse coding schemes applied in Raman distributed optical fiber\nsensing system are primarily classified into five categories, which specifically\ninclude the Simplex coding scheme, Pre-Shaped Simplex Coding scheme,\nlow-repetition-rate cyclic pulse coding scheme, Genetic-optimised aperiodic\ncoding scheme, Derived Sequences coding scheme.\nSimplex coding scheme, as a linear coding technique based on Hadamard\nmatrix transformation, has its code length (in L bits) determining the number of\ndetection signals required (L groups). For instance, in 2006, J. Park, et al.\nachieved a spatial resolution of 17.0 m, a temperature resolution of 3.0 °C, and a\ntotal of 2176 effective sensing points over a sensing distance of 37.0 km by\nutilizing this coding scheme and link optimization techniques [31].\nLow-repetition-rate cyclic pulse coding scheme generates Simplex\ncoding-based cyclic coding sequences using an acousto-optic modulator (AOM),\nenabling pulses to be injected into the optical fiber periodically at a low repetition\nrate. For example, in 2011, M. A. Soto, et al. combined the low-repetition-rate\nquasi-periodic cyclic pulse coding with a high-power fiber laser, achieving a\nspatial resolution of 1.0 m, a temperature resolution of 3.0 °C, and 26,000\neffective sensing points over a sensing distance of 26.0 km [27].\nPre-Shaped Simplex Coding scheme is based on simplex coding technology\nand adopts a linearly increasing profile to adjust pulse amplitude, compensating\nfor the amplitude variation caused by EDFA to suppress the transient effect of the\nEDFA and improve system performance. For example, in 2017, J. B. Rosolem, et\nal. achieved a spatial resolution of 10.0 m, a temperature resolution of 8.4 °C, and\n6,200 effective sensing points over a sensing distance of 62.0 km by using the\npre-shaped Simplex coding and a gain-controlled erbium-doped fiber amplifier\n[32].\nGenetic-optimised aperiodic coding scheme utilizes a distributed genetic\nalgorithm (DGA) to generate a single-sequence aperiodic code (GO-code), which\nis then converted into an optical pulse sequence and injected into the optical fiber.\nFor example, in 2020, X. Z. Sun, et al. achieved a spatial resolution of 1.0 m, a\ntemperature resolution of 3.9 °C, and 39,000 effective sensing points over a\nsensing distance of 39.0 km based on the Genetic-optimised aperiodic coding\nscheme [29].\nDerived Sequences coding scheme addresses the transient effect of EDFA\nthrough a derived sequence decoding method, thereby enhancing the performance\nof long-distance sensing. For instance, in 2022, D. D. Chai, et al. achieved a\nspatial resolution of 5.0 m, a temperature resolution of 2.5 °C, and 8,800 effective\nsensing points over a sensing distance of 44.0 km based on the Derived\nSequences coding scheme [33].”\n8) In the section of Experimental setup, page 9, right column, paragraph 3, line\n20, add “To ensure the environmental temperature stability of the sensing fiber\nduring the long-term experiment, the entire 70.0 km sensing fiber is placed in an\nultra-clean constant-temperature laboratory, where the ambient temperature is\nmaintained at 24.0±1.0 ℃. The FUT is placed in a high-precision\nconstant-temperature water bath with a temperature fluctuation of less than\n0.10 ℃. Thus, the above experimental setup can guarantee the temperature\nstability of the testing environment for the sensing fiber during long-term\nmeasurements.”\n9) In the section of Experimental results, page 14, change “Fig. 6, Fig .7” to “Fig.\n6”\nFig.6. Experimental comparison results of temperature sensing. (a1) Temperature\ndemodulation results at room temperature based on single-pulse scheme. (a2) Temperature\ndemodulation results at room temperature based on distorted detection signals. (a3) Temperature\ndemodulation results at room temperature based on proposed EAC-coding scheme. (b1) SNR based\non single-pulse scheme. (b2) SNR based on EAC-coding scheme (without pre-processing). (b3)\nSNR based on proposed EAC-coding scheme. (c1) Temperature resolution based on single-pulse\nscheme. (c2) Temperature resolution based on EAC-coding scheme (without pre-processing). (c3)\nTemperature resolution based on proposed EAC-coding scheme. (d1) Temperature demodulation\nresults at 50 ℃ based on EAC-coding scheme and EAC-coding scheme (without pre-processing).\n(d2) Temperature demodulation results at 70 ℃ based on EAC-coding scheme and EAC-coding\nscheme (without pre-processing). (d3) Temperature demodulation results at 90 ℃ based on\nEAC-coding scheme and EAC-coding scheme (without pre-processing).\n10) In the section of Experimental setup, page 8, right column, change “Fig. 2” to\n“Fig. 2”\nFig. 2. Experimental setup based on proposed EAC-coding scheme for Raman distributed\noptical fiber sensing.\n11) In the section of Experimental setup, page 10, left column, change “Fig. 3” to\n“Fig. 3”\nFig. 3. Timing of detection signals and autocorrelation function. (a1) Timing of the detection\nsignal 𝑢 before and after transient effects. (a2) Timing of the detection signal 𝑢̅ before and\nafter transient effects. (a3) Timing of the detection signal 𝑤 before and after transient effects.\n(a4) Timing of the detection signal 𝑤̅ before and after transient effects. (b1) Autocorrelation\nfunction of the detection signals before transient effects. (b2) Autocorrelation function of the\ndetection signals after transient effects.\n12) In the section of Introduction, page 2, right column, paragraph 2, line 3, add\n“Algorithm denoising schemes aim to improve the SNR of the system by\nprocessing optical fiber scattering signals. For example, M. Yu, et al. proposed a\ndynamic sampling-correction scheme achieving a sensing distance of 20.0 km [23].\nH. S. Pradhan, et al. proposed a Fourier wavelet regularised deconvolution\nscheme achieving a sensing distance of 30.0 km with a spatial resolution of 3.0 m\n[24]. Essentially derived from mathematical optimization theory, such schemes\nonly denoise signals from the perspective of signal processing without achieving\nbreakthroughs in physical mechanisms. Furthermore, they have limitations\nincluding parameter dependence and difficulty in preserving the true characteristics of\nsignals [30].\nIn addition, as one of the current mainstream denoising methods,\nconvolutional neural networks (CNNs) scheme is a typical data-driven approach.\nIt optimizes model parameters using large-scale training datasets, with the goal of\nachieving effective processing of test data. For example, Z. Zhang, et al. proposed\na deep 1-D denoising convolutional neural network scheme, which realized a\nsensing distance of 10 km with a spatial resolution of 3 m [26]. However, the\nperformance of this method is significantly constrained by the specificity of\ntraining data; when there is a notable distribution difference between test signals\nand the training set, its effect on enhancing sensing performance will be limited.”\n13) In the (unmodified manuscript) section of Introduction, page 3, left column,\nparagraph 2, line 3, delete“ In this work, an enhanced autocorrelation pulse\ncoding (EAC-coding) scheme is proposed, which introduces Golay\ncomplementary sequences into Raman distributed optical fiber sensing, and at the\nsame time restores the autocorrelation which is destroyed by the transient effects\nof erbium-doped fiber amplifier (EDFA) by preprocessing the Raman\nbackscattered signals for analysis and waveform-reconstruction. The proposed\nscheme further incorporates Haar wavelet denoising algorithm to enhance system\nperformance. In the experiment, a Raman distributed optical fiber sensing with\nsensing distance of 70.0 km, spatial resolution of 1.58 m and temperature\nresolution of 5.39 ℃ is achieved, which provides a new solution for the research\nof long-distance Raman distributed optical fiber sensing.”\n14) In the section of Introduction, page 4, left column, paragraph 3, line 22, add\n“Currently, existing pulse coding techniques in Raman distributed optical fiber\nsensing remain constrained by several prevalent bottlenecks: high hardware\nimplementation complexity, excessive computational overhead in encoding and\ndecoding, limited nonlinear effect suppression capability, and inadequate\nresistance to signal distortion coupled with poor stability during long-distance\ntransmission. Collectively, these factors constrain the system’s application\npotential in high-performance scenarios—including low SNR environments and\nlong-distance sensing applications.\nTo address the aforementioned issues, an Enhanced anti-distortion coding\n(EAC-coding) scheme is proposed in this paper. This scheme effectively\novercomes the trade-off dilemma among SNR, sensing distance, and hardware\ncost in traditional methods through a three-fold synergistic mechanism:\ncompensating for EDFA fluctuation via a preprocessing framework, suppressing\ntransmission losses through coding gain, and finely removing residual noise using\nwavelet transform. While maintaining relatively low complexity, the EAC-coding\nscheme significantly enhances the anti-distortion capability and adaptability of\nthe system, providing a new solution for long-distance, high-performance Raman\ndistributed optical fiber sensing. Experimental results demonstrate that at an\nultra-long distance of 70.0 km, the system achieves a spatial resolution of 1.58 m\nand a temperature resolution of 5.39 ℃, with the number of effective sensing\npoints reaching 44,303. To the best of our knowledge, this number of effective\nsensing points represents the highest level in the field of Raman distributed\noptical fiber sensing. In addition, the preprocessing architecture within\nEAC-coding (autocorrelation characteristic analysis, waveform analysis and\nreconstruction of Raman backscattered signals) significantly enhances the\ntemporal fidelity and transmission stability of encoded sequences by dynamically\ncompensating for EDFA transient gain fluctuation. This further improves the\nSNR and temperature measurement accuracy performance, enabling the\ntemperature measurement accuracy to reach 0.91 ℃, verifying the engineering\nfeasibility of the scheme.”\n15) In the (unmodified manuscript) section of Experimental results, page 10,\nright column, paragraph 2, line 29, delete “Raman distributed optical fiber\nsensing has emerged as a pivotal technology for continuous temperature\nmonitoring in long-range infrastructure and environmental applications. However,\nits practical implementation over distances exceeding 30 km has been\nfundamentally hindered by the inherently low signal-to-noise ratio (SNR) of\nRaman scattering signals, which creates a critical trade-off between sensing\ndistance and spatial resolution. In this study, we present a novel Raman\ndistributed optical fiber sensing system utilizing the proposed EAC-coding\nscheme, which effectively suppresses transient effects and significantly enhances\nthe SNR of system while incorporating Haar wavelet. This system enables\nlong-distance Raman distributed temperature measurement with high spatial\nresolution, achieving precise temperature demodulation and accurate\nidentification of FUT position and length. The experimental results demonstrate\nthat the proposed scheme achieves a spatial resolution of 1.58 m, temperature\nresolution of 5.39 ℃, and temperature measurement accuracy of 0.88 ℃ at the\nsensing distance of 70.0 km, establishing a new approach for long-distance\nRaman distributed optical fiber sensing system. Future research will integrate\nmore advanced denoising techniques to extend the system's sensing distance\nwhile preserving its spatial resolution capabilities.”\n16) In the section of Experimental results, page 18, left column, paragraph 2, line\n10, add “EAC-coding scheme proposed in this paper incorporates a novel\npreprocessing framework for autocorrelation characteristic analysis, waveform\nanalysis and reconstruction of Raman backscattered signals. The preprocessing\narchitecture for autocorrelation characteristic analysis, waveform analysis and\nreconstruction in this scheme can effectively suppress the transient effects\nintroduced by EDFA, thereby significantly improving the amplitude fidelity and\ntemporal stability of the encoded pulse sequence. This innovative active\nreconstruction mechanism in the signal domain, which is based on analyzing the\nwaveforms of Raman backscattered signals via forward/inverse Fourier\ntransforms, directly eliminates the phenomenon of detection pulse distortion\nexisting in traditional demodulation schemes. The scope of action of the\nEAC-coding scheme encompasses two key aspects: specifically, one is\naddressing the fundamental limitation of detection signal distortion through\nphysical-layer waveform reconstruction, and the other is performing correlation\noperations between the proposed coding sequence and the reconstructed Raman\nsignal to restore the ideal cross-correlation characteristics of Golay sequences,\nand achieve a theoretical gain value, thereby breaking through the SNR-distance\ntrade-off limit. It achieves the coordinated optimization of “waveform correction,\ncorrelation characteristic restoration, signal intensity enhancement”, laying a\nphysical layer foundation for long-distance sensing.\nFurthermore, the proposed EAC-coding scheme features a\nsynergistically enhanced two-stage noise suppression mechanism,\ndemonstrating innovations in multi-level joint denoising.\nFirst, EAC-coding scheme enhances the SNR of sensing signals through its\ninherent coding gain. Based on the cross-correlation characteristics of its\nsequence design, this coding scheme provides a significant inherent gain, which\ncompensates for signal attenuation caused by long-distance transmission and\neffectively improves the system's baseline SNR. Furthermore, this mechanism not\nonly significantly boosts optical power but also leverages the irrelevance between\nthe decoding algorithm and incoherent noise to achieve preliminary suppression of\ntransmission link losses at the encoding-decoding level.\nSecond, aiming at the residual noise with specific time-frequency domain\ndistribution characteristics in the decoded signal, this scheme further introduces\nHaar wavelet transform for adaptive noise filtering. The multi-resolution analysis\ncapability of the Haar wavelet enables accurate capture of the local\ntime-frequency features of noise. By performing sparse representation of the\nsignal at different scales (corresponding to different frequency bands) and\ntime-domain positions, it achieves effective separation between useful signals and\nnon-stationary noise components. While preserving the key details of the\ndistributed temperature signal, this method efficiently eliminates residual noise,\nsignificantly enhancing the clarity of the signal in the time-frequency domain and\nthe overall measurement accuracy of the system.\nThis three-fold synergistic mechanism, consisting of the preprocessing\nframework compensating for EDFA fluctuation, coding gain suppressing\ntransmission losses, and wavelet transform finely removing residual noise,\nsystematically breaks through the bottlenecks of traditional schemes in terms of\nSNR and sensing distance, providing a novel decoding framework for\nlong-distance and high-precision Raman distributed optical fiber sensing.”\n17) In the section of Experimental results, page 13, left column, paragraph 2, line\n18, add “In this study, a denoising algorithm based on the Haar wavelet is\nadopted to process distributed temperature sensing signals with abrupt change\ncharacteristics. The inherent step-like form of the Haar wavelet basis function\nendows it with excellent feature extraction capability for singular points in the\nsignal, especially for the abrupt temperature field change regions along the\nsensing fiber.”\n18) In the section of Introduction, page 3, left column, paragraph 3, line 27, add\n“The main limitation of this scheme lies in the linear growth of data acquisition\nvolume and computational complexity with code length, which restricts its\npractical efficiency in applications requiring long code lengths and high-speed\nsensing.”\n19) In the section of Introduction, page 3, right column, paragraph 1, line 9, add\n“However, higher pulse energy also makes it more likely to induce fiber\nnonlinear effects, and when approaching the stimulated scattering threshold, it\nrestricts the system’s sensing distance and SNR performance.”\n20) In the section of Introduction, page 3, right column, paragraph 2, line 25, add\n“Although this scheme effectively suppresses the transient response of the EDFA\nat the hardware level, its hardware structure is more complex, leading to a\nsignificant increase in implementation cost.”\n21) In the section of Introduction, page 4, left column, paragraph 1, line 3, add\n“The core challenge of this scheme lies in its high dependence on optimization\nalgorithms to search for the optimal code, which typically requires substantial\ncomputational resources and iterative testing.”\n22) In the section of Introduction, page 4, left column, paragraph 2, line 17, add\n“However, this scheme’s decoding process imposes a heavy computational\nburden, and the core algorithm involves high-complexity matrix operations,\nmaking it difficult to meet real-time requirements.”\n23) In the section of Discussion, page 19, right column, paragraph 4, line 7, add\n“Currently, the pulse coding techniques applied in Raman distributed optical fiber\nsensing system mainly include the following: Simplex coding scheme,\nPre-Shaped Simplex coding scheme, Low-repetition-rate cyclic pulse coding\nscheme, Genetic-optimised aperiodic coding scheme, and Derived Sequences\ncoding scheme. Their key performance indicators are presented in Table 2.\nTable 2. Sensing performance of various coding schemes.\nWe have compared our proposed scheme with other coding methods such as\nsimplex coding and Genetic-optimised aperiodic coding in terms of coding gain,\nmeasurement time, and system complexity. The specific revisions are as follows.\nIn terms of coding gain, the EAC-coding scheme proposed in this paper\nexhibits significant advantages in SNR improvement. The core of this scheme lies\nin the analysis and accurate reconstruction of the waveform of Raman\nbackscattered signals, which effectively compensates for the detection signals\ndistortion caused by the transient effects of the system. This mechanism enables\nEAC-coding to overcome the performance bottleneck of traditional derived\nsequences coding schemes induced by signals distortion, achieving a coding gain\ncloser to the theoretical limit. Specifically, existing derived sequence coding\nscheme construct coding sequences based on Golay complementary sequences\nand perform correlation decoding using their derived sequences. The upper limit\nof their theoretical coding gain is √L/2 (where L denotes the length of the coding\nsequence). However, due to the unavoidable distortion (especially transient\ndistortion) in actual detection signals, the results of their correlation operations\ndeteriorate, leading to a significant gap between the actually achieved coding gain\nand this theoretical value. In contrast, the EAC-coding scheme, through the\naforementioned signals analysis and reconstruction mechanism, significantly\nsuppresses the impact of transient distortion on the detection signals waveform,\nthereby enabling its coding gain to approach the theoretical upper limit of √L/2.\nBenefiting from this, the proposed system ultimately achieves temperature\nsensing capability in a long-distance Raman distributed optical fiber sensing\nsystem with a sensing distance of 70.0 km.\nIn terms of measurement time, the core advantage of the EAC-coding\nscheme stems from its extremely low decoding computational complexity. This\nscheme achieves signals reconstruction solely through Fourier transform, which\nsignificantly reduces the computational cost and time delay of real-time data\nprocessing, thereby effectively improving the overall response speed of the\nsystem. Specifically, for a Simplex code with length L, it is necessary to inject L\ngroups of detection signals into the optical fiber and collect L groups of Raman\nbackscattered signals, with its theoretical minimum acquisition time being\nT =L×t (where t denotes the acquisition time of one group of Raman\nSimplex\nbackscattered curves). Although the Genetic-optimised aperiodic coding scheme\nonly requires injecting one group of detection signals into the optical fiber, it\nneeds additional time to design the coding sequence based on the distributed\ngenetic algorithm. The Derived sequences coding scheme requires injecting 4\ngroups of detection signals into the optical fiber, with a theoretical acquisition\ntime of 4t. However, in the decoding stage, it involves complex steps such as\nextracting the attenuation envelope, establishing a compensation model, and\nsolving the compensation envelope via matrix operations, which increases the\ntime cost of the decoding process. The EAC-coding scheme proposed in this\npaper performs encoding based on Golay complementary sequences, with a\ntheoretical acquisition time of 4t, and only needs Fourier transform to complete\nthe analysis and reconstruction of the Raman backscattered signals waveform.\nThis significant efficiency improvement at the algorithm level greatly reduces the\nreal-time data processing delay and effectively enhances the system response\nspeed, providing crucial real-time guarantee for the final realization of\ntemperature sensing in a 70.0 km long-distance Raman distributed optical fiber\nsensing system.\nIn terms of system complexity, the core innovation of the EAC-coding\nscheme lies in achieving a high degree of simplification in the decoding process\nthrough algorithm optimization, while keeping the hardware architecture\nunchanged. This scheme only needs to perform efficient Fourier transform\noperations to complete signal reconstruction, which significantly reduces the\nalgorithmic complexity and computational burden of real-time data processing.\nThe specific reasons are as follows. Simplex coding scheme requires the injection\nof L groups of detection signals, resulting in a long acquisition time and a large\nvolume of raw data. This not only imposes high requirements on hardware\nperformance (such as data acquisition rate and storage capacity) and long-term\nstability, but also the large-scale data processing involved in its decoding process\nsignificantly increases the computational complexity. Genetic-optimised\naperiodic coding scheme greatly shortens the acquisition time without increasing\nhardware costs. However, due to its unique design, it is necessary to design\ncoding sequences based on a distributed genetic algorithm and conduct extensive\ntests to find the optimal coding sequence. Derived sequences coding scheme also\ndoes not require additional hardware overhead. However, this scheme introduces\nhigh computational complexity in the decoding stage, as it relies on\ncomputationally expensive matrix operations to generate and process derived\nsequences.\nEAC-coding scheme proposed in this paper incorporates a novel\npreprocessing framework for autocorrelation characteristic analysis, waveform\nanalysis and reconstruction of Raman backscattered signals. This framework\nsignificantly improves the fidelity and transmission stability of the encoded pulse\nsequence by dynamically compensating for the transient gain fluctuation of\nEDFA. This technology leverages the inherent gain of EAC-coding pulse coding\nto effectively offset fiber scattering attenuation during 70.0 km long-distance\ntransmission, achieving a significant improvement in the baseline SNR. On this\nbasis, a two-stage noise suppression method is further constructed. The first-stage\nprocessing involves compensating for signal attenuation using the theoretical\ncoding gain of EAC-coding. For the second-stage processing, a Haar wavelet\ndenoising algorithm is adopted. Its step-matching characteristic enables accurate\nextraction of the abrupt temperature change features of the sensing fiber and\nadaptive filtering of the residual time/frequency domain coupled noise in the\ndecoded signal. This three-fold synergistic mechanism, consisting of the\npreprocessing framework compensating for EDFA fluctuation, coding gain\nsuppressing transmission losses, and wavelet transform finely removing residual\nnoise, breaks through the theoretical trade-off bottleneck between SNR and\nsensing distance in traditional schemes. Experiment results indicate that, at an\nultra-long distance of 70.0 km, this scheme can achieve a spatial resolution of\n1.58 m, a temperature resolution of 5.39 °C, and an effective number of sensing\npoints reaching 44,303, verifying the engineering feasibility of the scheme. To the\nbest of our knowledge, the number of effective sensing points achieved by this\nscheme ranks the highest in the field of Raman distributed optical fiber sensing\nsystems.”\n24) In the section of Experimental setup, page 9, left column, paragraph 2, line\n21, add “Furthermore, the measurement time of the scheme proposed in this paper is\nmainly limited by the massive data volume (with the effective number of sensing\npoints reaching 44,303) and the hardware accumulation processing time of the\nacquisition card, which are caused by its long sensing distance and high spatial\nresolution—rather than the complexity of its processing architecture. The current\nmeasurement time (252 min) is constrained by the processing capability of the\ndata acquisition card (acquisition rate: 1.0 GSa/s; storage depth: 512 Mpts). The\nmassive data volume (approximately 700 k points per frame corresponding to a\n70.0 km sensing distance) exceeds the on-board real-time processing limit. In the\nfuture, high-performance acquisition cards will be upgraded to optimize the data\nprocessing pipeline, thereby eliminating the delay deterioration caused by\nhardware bottlenecks.”\n25) In the section of Discussion, page 21, right column, paragraph 3, line 35, add\n“In this proposed scheme, the physical limitations on the optimization of sensing\ndistance and SNR mainly stem from two aspects: the insufficient performance of\nexperimental devices and the physical demodulation principle.\nIn terms of experimental devices, the maximum coding bit length of the\ndigital delayed pulse generator (DDPG) and the sampling rate of the data\nacquisition card are key factors restricting the improvement of the sensing\ndistance and SNR of this scheme. The CIQTEK ASG8100 model DDPG used in\nthe experiment has a maximum coding bit length of 99 bits. Since the bit length\nof Golay complementary sequences is typically 2ⁿ, a coding length of 64 bits was\nselected in the experiment. The coding length directly determines the coding gain\nof the system, which in turn affects the extent of improvement in sensing\nperformance. Therefore, it is planned to adopt a DDPG with a higher maximum\ncoding bit length (e.g., ≥128 bits) in the future to increase the system's coding\nlength, thereby achieving better sensing distance performance. In addition, the\ncurrently used data acquisition card has a sampling rate of 1.0 GSa/s and a\nmaximum number of sampling points of 700,000, corresponding to a theoretical\nmaximum sensing distance of approximately 70.0 km. Future plans involve\nupgrading to a data acquisition card with a higher sampling rate (e.g., ≥2 GSa/s)\nand a larger number of sampling points (e.g., ≥1,000,000) to eliminate the\nlimitations imposed by hardware devices on the sensing distance.\nIn terms of the physical demodulation principle, the stimulated scattering\nthreshold and fiber dispersion effect also affect the improvement of sensing\ndistance and SNR in this scheme. Firstly, the stimulated scattering threshold of\nsingle-mode fibers is relatively low, which limits the maximum optical power\ninjected into the fiber. As a result, the intensity of the Raman backscattered signal\nexcited in the fiber is relatively weak, leading to a low SNR. In the future, we will\nattempt to use few-mode fibers to increase the optical power injected into the\nfiber while minimizing intermodal dispersion as much as possible. Finally, fiber\ndispersion introduced by long-distance transmission causes pulse broadening and\nintersymbol interference, which destroys the orthogonality of sequences. This\nresults in the broadening of demodulated correlation peaks and a reduction in\ntheir amplitude, impairing both SNR and distance resolution. This issue can be\ncompensated for by introducing dispersion-compensating fibers.”\n26) In the section of Experimental results, page 13, left column, paragraph 2, line\n26, add “The Haar wavelet function generates a set of orthogonal basis functions\nthrough translation and scaling, enabling multi-scale decomposition of signals. Its\ninherent advantage in processing low-complexity signals with abrupt change\ncharacteristics makes it particularly suitable for the analysis of Raman\nbackscattered signals.\nIn the experiment, to further improve the SNR of Raman backscattered\nsignals, we adopted a 6-level decomposition Haar wavelet. Furthermore, in the\npost-processing stage of temperature demodulation, to further suppress noise and\nenhance signal smoothness, we additionally applied the db10 (Daubechies\nwavelet 10) wavelet function with 4-level decomposition. It should be noted that\nwhile this step improves signal quality (by reducing temperature fluctuation), it\nmoderately degrades the spatial resolution of the system. Such parameter\nadjustment reflects the necessary trade-off between spatial resolution and\ntemperature measurement accuracy.”\n27) In the section of Experimental results, page 15, left column, paragraph 2, line\n28, add “Temperature fluctuation is expressed as the difference between the\nmeasured temperature and the ambient temperature. Specifically, in a Raman\ndistributed fiber optic sensing system, there exists a discrepancy between the\ndemodulated temperature (T') at the sampling points of the sensing fiber and the\nambient reference temperature (T₀). This discrepancy is defined as temperature\nfluctuation (ΔT=T'－T₀).”\n28) In the section of Experimental results, page 16, left column, paragraph 3, line\n29, add “Temperature resolution refers to temperature uncertainty, which\ncharacterizes the system's ability to distinguish temperature changes, is generally\ndefined as the standard deviation (σ) of measured temperatures under constant\ntemperature conditions (e.g., a section of reference fiber) [34-35].”\n29) In the section of Experimental results, page 13, left column, paragraph 1, line\n10, add “(with Haar wavelet).”\n30) In the section of Experimental results, page 11, left column, change “Fig. 4” to\n“Fig. 4”.\nFig. 4. Intensity of Raman backscattered signals and SNR. (a1) Intensity of Raman\nbackscattered signal generated by detection signal 𝑢 before and after pre-processing. (a2)\nIntensity of Raman backscattered signal generated by detection signal 𝑢̅ before and after\npre-processing. (a3) Intensity of Raman backscattered signal generated by detection signal 𝑤\nbefore and after pre-processing. (a4) Intensity of Raman backscattered signal generated by\ndetection signal 𝑤̅ before and after pre-processing. (b1) Intensity of Raman backscattered\nsignals decoded by distorted detection signals before and after pre-processing. (b2) SNR of\nRaman backscattered signals decoded by detection signals before and after pre-processing.\n(c1) Autocorrelation function of the detection signals before pre-processing. (c2)\nAutocorrelation function of the distorted detection signals after pre-processing.\n31) In the section of Experimental results, page 12, left column, paragraph 2, line\n3, add “We have added an autocorrelation processing experiment on the\ndetection signals coupled into the sensing fiber after reconstruction, aiming to\nfurther verify that it eliminates the transient effects of the system. The details of\nthe newly added experiment are as follows. The primary objective of the newly\nadded experiment is to verify that the reconstructed Raman backscattered signals\nis equivalent to the Raman backscattered signal of the undistorted detection\nsignals.\nTaking the detection signal u as an example, its attenuation envelope\nfunction can be expressed by Eq. (8). Thus, the detection signal coupled into the\nsensing fiber after reconstruction can be calculated and is given by Eq. (17).\nu  = i f f t (\nf f t\nf\n u\nf t (\n(\nf\nf )\n)\n\n)\n) (17)\nThen, we performed the same processing on the four detection signals and\nconducted autocorrelation operations on the processed detection signals. If Eq.\n(18) is satisfied, it can be verified that their autocorrelation characteristics are\nrestored after reconstruction, with the transient effects effectively suppressed.\n(u−u)(u−u)+(w−w)(w−w)=2l (18)\nThe experimental results are shown in Fig. 4. Fig. 4 (c1) presents the\nautocorrelation function of the detection signals with waveform distortion caused\nby transient effects, while Fig. 4(c2) shows the autocorrelation function of the\nequivalent detection signals coupled into the sensing fiber after reconstruction. It\ncan be clearly observed from Fig. 4(c2) that the sidelobe noise of its\nautocorrelation function is significantly reduced, which verifies that its\nautocorrelation characteristics are restored and the transient effects are effectively\nsuppressed.”\n32) In the (unmodified manuscript) section of Experimental results, page 9, right\ncolumn, paragraph 2, line 15, delete “The SNR measurement result after\ndecoding is shown in Fig. 6(a). Compared with the conventional single-pulse\nscheme, the SNR at 70.0 km of sensing fiber is improved by 8.75 dB based on\nproposed EAC-coding scheme, which validates the superiority of the proposed\nEAC-coding scheme in SNR improvement.\nThe temperature demodulation result is shown in Fig. 6(b).\nExperimental measurement demonstrates that the proposed\nEAC-coding scheme achieves significant suppression of temperature\nfluctuation under ambient conditions, reducing the temperature\nuncertainty from ±300 ℃ maximum in the conventional single-pulse\nscheme to ±15.84 ℃.\nFurthermore, we conduct additional quantitative analyses by\nevaluating the temperature resolution of the system.\nThe temperature resolution based on the conventional single-pulse scheme\nand proposed EAC-coding scheme are shown in Fig. 7(a). At the sensing distance\nof 70.0 km, the conventional single-pulse scheme achieves a temperature\nresolution of 29.25 ℃. In contrast, the proposed EAC-coding scheme\ndemonstrates significant performance enhancement by effectively improving the\nSNR, which substantially reduces system temperature fluctuation,\nresulting in a remarkable improvement of temperature resolution to\n5.39 ℃ at the same sensing distance. Meanwhile, to validate the\nspatial resolution of the proposed EAC-coding scheme, a 40-meter-long fiber under test is positioned at the distance of 70.0\nkm and immersed in a thermostatically controlled water bath maintained\nat 90 ℃, while the remaining portion of the sensing fiber is exposed to the room\ntemperature of 20 ℃”.\n33) In the section of Experimental results, page 15, left column, paragraph 2, line\n5, add “The results of temperature demodulation and SNR are presented in Fig. 6.\nThe temperature fluctuation of the traditional single-pulse scheme can be as high\nas approximately 300 ℃, as shown in Fig. 6(a1). In this paper, first, by\nleveraging the synergistic demodulation mechanism integrating EAC-coding\n(which compensates for attenuation via coding gain) and the refined processing of\nHaar wavelet denoising, effective suppression of temperature fluctuation noise\nalong the optical fiber is achieved. This significantly reduces the system’s\ntemperature fluctuation to 22.51 ℃ while improving the SNR by 7.24 dB, as\nshown in Fig. 6(a2) and Fig. 6(b2). Furthermore, the preprocessing architecture\nwithin EAC-coding (autocorrelation characteristic analysis, waveform analysis\nand reconstruction of Raman backscattered signals) further reduces the system’s\ntemperature fluctuation to 20.86 ℃ by dynamically compensating for EDFA\ntransient gain fluctuation and reconstructing Raman scattered signals. Meanwhile,\nthe SNR is further improved by an additional 1.48 dB, as shown in Fig. 6(a3) and\nFig. 6(b3).\nCompared with the temperature resolution of 29.25 ℃ achieved by the\ntraditional single-pulse scheme, the EAC-coding scheme (integrating coding gain\nwith Haar wavelet denoising) improves the system’s temperature resolution to\n5.82 ℃, as shown in Fig. 6(c2). Meanwhile, the preprocessing architecture within\nEAC-coding further enhances the system’s temperature resolution to 5.39 ℃ by\ndynamically compensating for EDFA transient gain fluctuation and\nreconstructing Raman scattered signals, as shown in Fig. 6(c3).\nMeanwhile, we further compared the temperature measurement\naccuracy performance of the system, as shown in Fig. 6(d1) - (d3). It can be\nobserved that the transient effects not only affect the SNR, temperature\nfluctuation, and temperature resolution but also exert a significant impact on\nthe system’s temperature measurement accuracy. It can be observed that as the\ntemperature of the fiber under test (FUT) gradually increases, the temperature\nmeasurement error of the distorted signal demodulation results becomes\nincreasingly large. This confirms that the influence of the transient effect also\nintensifies with rising temperature—with the temperature measurement accuracy\ndeteriorating to a maximum of 14.98 °C at 90.0 °C (where the demodulation\nresult is 104.98 °C). This is because with increasing temperature, the elevation of\nthe Raman backscattered curve at the FUT becomes more pronounced, while\ntransient effects exert an increasingly significant influence on signal intensity.\nAfter the preprocessing architecture in the EAC-coding scheme (autocorrelation\ncharacteristic analysis, waveform analysis and reconstruction of Raman\nbackscattered signals), the temperature demodulation result is 90.91 ℃, and the\ntemperature measurement accuracy is 0.91 ℃, representing an improvement of\napproximately 16.46 times. Therefore, the EAC-coding scheme proposed in this\npaper can effectively improve the system’s temperature measurement accuracy,\nenhancing the temperature measurement accuracy of the long-distance Raman\ndistributed optical fiber sensing system (with a sensing distance of 70.0 km) to\nwithin 1.0 ℃.\nThrough the synergistic demodulation mechanism of\nEAC-coding (which utilizes coding gain to compensate for\nattenuation) combined with the refined processing of Haar wavelet\ndenoising, the theoretical trade-off bottleneck between SNR and\nsensing distance in traditional schemes is broken through.\nExperimental results demonstrate that at an ultra-long distance of\n70.0 km, the system achieves a spatial resolution of 1.58 m and a\ntemperature resolution of 5.39 ℃. Moreover, the preprocessing\narchitecture in EAC-coding (integrating autocorrelation\ncharacteristic analysis of Raman backscattered signals and\nwaveform analysis and reconstruction) significantly enhances the\ntemporal fidelity and transmission stability of coded pulse sequences\nby dynamically compensating for EDFA transient gain fluctuation.\nThis further improves the system's SNR and temperature\nmeasurement accuracy, enabling the temperature measurement\naccuracy to reach 0.91 ℃. In this study, the improvements in SNR\n(accompanied by performance enhancements in sensing distance and\ntemperature resolution) are primarily attributed to the proposed\nEAC-coding (for coding gain compensation) and Haar wavelet\ndenoising schemes. In contrast, the preprocessing architecture within\nEAC-coding (characterized by autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered\nsignals) serves to improve the system's temperature measurement\naccuracy by dynamically compensating for EDFA transient gain\nfluctuation and reconstructing Raman scattered signals.”\n34) In the section of Principles and methods, page 5, change “Fig. 1” to “Fig. 1”.\nFig. 1. Physics principle of proposed EAC-coding scheme for Raman distributed optical\nfiber sensing. (a) Principle of encoding based on Golay complementary sequences. (b) The\ninfluence of transient effects on Raman backscattered signals. (c)RBSs generated by four\ndistorted detection signals in sensing fiber; (d) Principle of decoding after analysis and\nwaveform-reconstruction based on proposed EAC-coding scheme. (e) Temperature\ndemodulation principle.\n35) In the section of Principles and methods, page 5, left column, paragraph 3,\nline 18, change “destroyed detection signals” to “distorted detection signals”.\n36) In the section of Experimental results, page 11, right column, paragraph 2,\nline 20, change “destroyed detection signals” to “distorted detection signals”.\n37) In the section of Experimental results, page 11, right column, paragraph 2,\nline 27, change “destroyed detection signals” to “distorted detection signals”.\n38) In the section of Discussion, page 22, right column, paragraph 3, line 18, add\n“For the coding technology with a code length of 64 bits (i.e., the EAC-coding\nscheme adopted in this paper). Under the maximum input power achievable by a\nsingle pulse demodulation system (0.2 mW), the theoretical SNR improvement is\n6 dB.\nHowever, the theoretical 6 dB SNR improvement is based on the strict\npremise that the input powers of the single-pulse demodulation scheme and the\npulse coding scheme are the same. In this experiment, to explore the extreme\nperformance of the EAC-coding scheme and maximize the system SNR, we set\nthe input power to be close to the maximum value of the stimulated Raman\nscattering (SRS) nonlinear effect threshold of the sensing fiber. Specifically, the\naverage power input into the optical fiber is approximately 0.7 mW, and the\ncalculated peak power is close to 1.4 W.\nIn contrast, the traditional single-pulse demodulation scheme, due to its\nhigher peak power (under the same average power), is more likely to trigger the\nSRS nonlinear effect, leading to signal distortion and performance degradation.\nTherefore, to ensure the stable operation of the single-pulse scheme below the\nnonlinear threshold, its average input power must be significantly reduced, which\nis set to approximately 0.2 mW in the experiment.\nThe different incident powers of the two schemes are incorporated into the\ncalculation of the theoretical SNR improvement. According to Eq. (4) in the\npaper, with all other factors remaining completely unchanged, the intensity of the\nRaman backscattered signal depends solely on the incident optical power. Thus,\nthe modified theoretical SNR improvement is approximately\n10log\n10\n[(√64/2)×(0.7/0.2)]= 11.46 dB. Since the EDFA introduces a significant\namount of amplified spontaneous emission (ASE) noise while amplifying the\neffective signal, the final experimental improvement in SNR is 8.72 dB, which is\nslightly lower than the theoretical value of 11.46 dB.\nIn summary, it is precisely because the EAC-coding scheme allows a higher\naverage input power without triggering significant nonlinear effects, and\ncombined with its inherent theoretical coding gain, the SNR improvement\nobserved in the experiment finally reaches 8.72 dB, which is slightly lower than\nthe theoretical SNR coefficient (11.46 dB) at this power setting (0.7 mW).”\n39) In the section of Discussion, page 15, right column, paragraph 2, line 5, add\n“In the experiment, within a range from the starting end of the sensing fiber to\n56.0 km, the SNR improvement of the sensing signal is about 10.44 dB; while in\nthe region beyond approximately 70.0 km at the tail end of the optical fiber, the\nSNR improvement is 8.72 dB. The improvement of SNR at each sensing distance\npoint is lower than the theoretical value of 11.46 dB. The improvement of SNR at\nthe end of sensing fiber is also lower than that at the front end of sensing fiber.\nThis discrepancy primarily stems from the synergistic effect between the\ndifference in SNR improvement between experiments and theory conditions, and\nthe distance-dependent characteristics of fiber attenuation.\nAfter revising the SNR calculation formula, the overall SNR improvement\nalong the optical fiber obtained from the experimental results is slightly lower\nthan the theoretical SNR. Since the maximum input optical power of the sensing\nfiber affects the theoretical SNR improvement of its coding scheme, the final\nSNR magnitude calculated for the EAC-coding scheme is 11.46 dB. Meanwhile,\ndue to the introduction of the EDFA, a large amount of amplified spontaneous\nemission (ASE) noise is introduced during the process of amplifying the detection\nsignal—this results SNR improvement in the experiment being slightly lower\nthan the theoretical value of 11.46 dB. Consequently, the SNR improvement\nalong the optical fiber derived from the experimental results (with a maximum of\n10.44 dB) is slightly lower overall than the theoretical SNR (11.46 dB).\nFurthermore, fiber attenuation exhibits a cumulative effect with transmission\ndistance. At 70.0 km, the single-pulse signal is already close to the system’s\ndetection limit due to severe attenuation, making it difficult to extract effectively.\nAlthough the EAC-coding scheme still maintains a certain signal advantage, the\nintensity difference between the EAC-coding signal and the single-pulse signal is\nsmaller than that at 28.0 km, as the signal amplitude decreases significantly after\nlong-distance transmission. Consequently, the SNR improvement at this location\ndecreases to 8.72 dB. This result clearly reflects the distance-dependent\ncharacteristic of fiber signal attenuation and also highlights the performance\ndifference of the coding scheme at different transmission distances.”\n40) In the section of Experimental results, page 16, right column, paragraph 3,\nline 37, add “In this experiment, temperature resolution is characterized by the\ntemperature standard deviation of each distributed temperature measurement\npoint within a fixed length of the sensing fiber. Experimental results show that at\na sensing distance of 70.0 km, the temperature resolution of the EAC-coding\nscheme is significantly improved compared with that of the single-pulse scheme:\nthe temperature resolution is enhanced from 29.25 °C (of the single-pulse scheme)\nto 5.39 °C, representing an improvement of up to 5.43 times.”\n41) In the (unmodified manuscript) section of References, page 12, right column,\ndelete “[21] M. A. Soto, et al. Raman-based distributed temperature sensor with\n1 m spatial resolution over 26 km SMF using low-repetition-rate cyclic pulse\ncoding. Opt. Lett. 36(13), 2557-2559 (2011).\n[22] G. D. B. Vazquez, et al. Distributed temperature sensing using cyclic\npseudorandom sequences. IEEE Sens. J. 17(6), 1686-1691 (2017).\n[23] X. Z. Sun, et al. Genetic-optimised aperiodic code for distributed\noptical fibre sensors. Nat. Commun. 11(1), 5774 (2020).\n[24] Z. L. Wang, et al. Application of wavelet transform modulus maxima in\nRaman distributed temperature sensors. Photonic Sens. 4, 142-146(2014).\n[25] Z. L. Wang, et al. An improved denoising method in RDTS based on\nwavelet transform modulus maxima. IEEE Sens. J. 15(2), 1061-1067 (2015).\n[26] M. Yu, et al. Ambient condition desensitization of a fiber Raman\ntemperature sensing system based on a dynamic sampling-correction scheme.\nAppl. Opt. 54(15), 4823-4827(2015).\n[27] H. S. Pradhan, et al. Characterisation of Raman distributed temperature\nsensor using deconvolution algorithms. IET Optoelectron. 9(2), 101-107(2015).\n[28] H. S. Guo, et al. High Precision Raman Distributed Fiber Sensing\nUsing Residual Composite Dual-Convolutional Neural Network. J. Lightwave\nTechnol. 42(10), 3918-3928 (2024)\n[29] Z. Zhang, et al. High-performance Raman distributed temperature\nsensing powered by deep learning. J. Lightwave Technol. 39(2), 654-659(2020).\n[30] Y. Liu, et al. Long-range Raman distributed temperature sensor with\nhigh spatial and temperature resolution using graded-index few-mode fiber. Opt.\nExpress. 26(16), 20562-20571 (2018).\n[31] M. Wang, et al. Few-mode fiber-based Raman distributed temperature\nsensing. Opt. Express. 25(5), 4907-4916 (2017).\n[32] H. Wu, et al. 24 km High-performance Raman distributed temperature\nsensing using low water peak fiber and optimized denoising neural network.\nSensors. 22(6), 2139 (2022)”\n42) In the section of References, page 24, right column, add “[21] Z. L. Wang, et\nal. Application of wavelet transform modulus maxima in Raman distributed\ntemperature sensors. Photonic Sens. 4, 142-146 (2014).\n[22] Z. L. Wang, et al. An improved denoising method in RDTS based on\nwavelet transform modulus maxima. IEEE Sens. J. 15(2), 1061-1067 (2015).\n[23] M. Yu, et al. Ambient condition desensitization of a fiber Raman\ntemperature sensing system based on a dynamic sampling-correction scheme.\nAppl. Opt. 54(15), 4823-4827 (2015).\n[24] H. S. Pradhan, et al. Characterisation of Raman distributed temperature\nsensor using deconvolution algorithms. IET Optoelectron. 9(2), 101-107 (2015).\n[25] H. S. Guo, et al. High Precision Raman Distributed Fiber Sensing\nUsing Residual Composite Dual-Convolutional Neural Network. J. Lightwave\nTechnol. 42(10), 3918-3928 (2024)\n[26] Z. Zhang, et al. High-performance Raman distributed temperature\nsensing powered by deep learning. J. Lightwave Technol. 39(2), 654-659 (2020).\n[27] M. A. Soto, et al. Raman-based distributed temperature sensor with 1 m\nspatial resolution over 26 km SMF using low-repetition-rate cyclic pulse coding.\nOpt. Lett. 36(13), 2557-2559 (2011).\n[28] G. D. B. Vazquez, et al. Distributed temperature sensing using cyclic\npseudorandom sequences. IEEE Sens. J. 17(6), 1686-1691 (2017).\n[29] X. Z. Sun, et al. Genetic-optimised aperiodic code for distributed\noptical fibre sensors. Nat. Commun. 11(1), 5774 (2020).\n[30] L. Xu, et al. RDTS noise reduction method based on\nICEEMDAN-FE-WSTD. IEEE Sens. J. 22(18), 17854-17863 (2022).\n[31] J. Park, et al. Raman-based distributed temperature sensor with simplex\ncoding and link optimization. IEEE Photonics Technol. Lett. 18(17), 1879-1881\n(2006).\n[32] B. Rosolem, et al. Raman DTS based on OTDR improved by using\ngain-controlled EDFA and pre-shaped simplex code. IEEE Sens. J. 17(11),\n3346-3353 (2017).\n[33] D. D. Chai, et al. Derived sequences decoding approach for long-range\ndistributed temperature sensors. IEEE Sens. J. 23(3), 2204-2210 (2022).\n[34] X. Liu, et al. High-speed and high-resolution YAG fiber based\ndistributed high temperature sensing system empowered by a 2D image\nrestoration algorithm. Opt. Express. 31(4), 6170-6183 (2023).\n[35] J. Gasser, et al. Distributed temperature sensor combining centimeter\nresolution with hundreds of meters sensing range. Opt. Express. 30(5), 6768-6777\n(2022).”\nAgain, we are grateful for the insightful suggestions from the reviewers.\nSincerely Yours,\nJian Li, Mingjiang Zhang\nResponse to the reviewers’ comments\nThank you very much for your consideration of our manuscript entitled “70 km Long-\nRange Raman Distributed Optical Fibre Sensing Through Enhanced Anti-distortion\nCoding and Waveform Reconstruction” by Fan Zhang, Jian Li, Lulei Li, Kangyi Cao\nand Mingjiang Zhang.\nWe would like to thank the reviewers for their efforts to review our manuscript and their\nappreciation of the novelty and quality of our work. The constructive suggestions from\nthe reviewers have been thoroughly considered and implemented in the revised\nmanuscript, which now has been significantly improved.\nIn the next several pages, the changes made to the manuscript are detailed to fully\naddress the concerns raised according to each of the reviewers’ comments. We hope the\nmanuscript is now appropriate for publication in Nature Communications.\nIn addition, we would like to declare:\n(1) All authors agree with the submission.\n(2) The work has not been published or submitted for publication elsewhere, either\ncompletely or in part, or in another form or language.\n(3) No materials are reproduced from another source.\n(4) The authors declare no conflicts of interest.\nWe look forward to hearing from you!\nWith best regards,\nJian Li, Mingjiang Zhang\nAll the reviewers’ suggestions have been considered. The following are the changes\nmade in the manuscript to fully address the reviewers’ concerns:\nBlue: Original comments from the reviewer.\nBlack: Our response including action taken.\nResponds to the reviewers’ comments:\nReviewer 1 (Comments to the Author):\nRecommendations for the Author(s):\nMy comments have been well addressed, and all the questions have been answered in\ndetail. The current manuscript can be accepted for publication.\nReply: We sincerely appreciate your careful and thorough review and\npositive feedback. Your detailed questions and constructive guidance have\nbeen invaluable in refining the manuscript. We feel greatly honored and\nencouraged to receive the “accept for publication” decision. Once again, we\nwould like to extend our sincere gratitude to you.\nResponds to the reviewers’ comments:\nReviewer 2 (Comments to the Author):\nRecommendations for the Author(s):\nI can see that the authors have been trying very hard to carefully address all the\ncomments that the reviewers raised. While all the comments have been\ncomprehensively discussed, the current manuscript is way too lengthy, especially for\nthe introduction and the discussion parts. Much of the content should be much more\nconcise or moved to the supplementary material.\nReply: We sincerely appreciate your careful review and constructive\nfeedback on our manuscript. Your recognition of our earnest efforts to address\nall the previous comments is truly encouraging, and we are grateful for your\nthoughtful insights that help refine the work further.\nFollowing your valuable suggestions, we have substantially streamlined\nredundant content and relocated relevant materials to the Supplementary\nInformation, ensuring that the core information of the study remains concise\nand focused while retaining all critical information.\nThank you for your suggestion. We have made the following\nmodifications in our revised manuscript:\n1) In the section of Introduction, the following content has been\nrelocated to the Supplementary Information. “Simplex\ncoding scheme, as a linear coding technique based on Hadamard\nmatrix transformation, has its code length (in L bits) determining the\nnumber of detection signals required (L groups). For instance, in 2006,\nJ. Park, et al. achieved a spatial resolution of 17.0 m, a temperature\nresolution of 3.0 °C, and a total of 2176 effective sensing points over\na sensing distance of 37.0 km by utilizing this coding scheme and link\noptimization techniques. The main limitation of this scheme lies in\nthe linear growth of data acquisition volume and computational\ncomplexity with code length, which restricts its practical efficiency in\napplications requiring long code lengths and high-speed sensing.\nLow-repetition-rate cyclic pulse coding scheme generates\nSimplex coding-based cyclic coding sequences using an acousto-\noptic modulator (AOM), enabling pulses to be injected into the optical\nfiber periodically at a low repetition rate. For example, in 2011, M. A.\nSoto, et al. combined the low-repetition-rate quasi-periodic cyclic\npulse coding with a high-power fiber laser, achieving a spatial\nresolution of 1.0 m, a temperature resolution of 3.0 °C, and 26,000\neffective sensing points over a sensing distance of 26.0 km. However,\nhigher pulse energy also makes it more likely to induce fiber nonlinear\neffects, and when approaching the stimulated scattering threshold, it\nrestricts the system’s sensing distance and SNR performance.\nPre-Shaped Simplex Coding scheme is based on simplex coding\ntechnology and adopts a linearly increasing profile to adjust pulse\namplitude, compensating for the amplitude variation caused by EDFA\nto suppress the transient effect of the EDFA and improve system\nperformance. For example, in 2017, J. B. Rosolem, et al. achieved a\nspatial resolution of 10.0 m, a temperature resolution of 8.4 °C, and\n6,200 effective sensing points over a sensing distance of 62.0 km by\nusing the pre-shaped Simplex coding and a gain-controlled erbium-\ndoped fiber amplifier. Although this scheme effectively suppresses\nthe transient response of the EDFA at the hardware level, its hardware\nstructure is more complex, leading to a significant increase in\nimplementation cost.\nGenetic-optimised aperiodic coding scheme utilizes a distributed\ngenetic algorithm (DGA) to generate a single-sequence aperiodic\ncode (GO-code), which is then converted into an optical pulse\nsequence and injected into the optical fiber. For example, in 2020, X.\nZ. Sun, et al. achieved a spatial resolution of 1.0 m, a temperature\nresolution of 3.9 °C, and 39,000 effective sensing points over a\nsensing distance of 39.0 km based on the Genetic-optimised aperiodic\ncoding scheme. The core challenge of this scheme lies in its high\ndependence on optimization algorithms to search for the optimal code,\nwhich typically requires substantial computational resources and\niterative testing.\nDerived Sequences coding scheme addresses the transient\neffects of EDFA through a derived sequence decoding method,\nthereby enhancing the performance of long-distance sensing. For\ninstance, in 2022, D. D. Chai, et al. achieved a spatial resolution of\n5.0 m, a temperature resolution of 2.5 °C, and 8,800 effective sensing\npoints over a sensing distance of 44.0 km based on the Derived\nSequences coding scheme. However, this scheme’s decoding process\nimposes a heavy computational burden, and the core algorithm\ninvolves high-complexity matrix operations, making it difficult to\nmeet real-time requirements.”\n2) In the section of Discussion, the following content has been\nrelocated to the Supplementary Information. “We have compared\nour proposed scheme with other coding methods such as simplex\ncoding and Genetic-optimised aperiodic coding in terms of coding\ngain, measurement time, and system complexity. The specific revisions are as follows.\nTable 2. Sensing performance of various coding schemes.\nIn terms of coding gain, the EAC-coding scheme proposed in\nthis paper exhibits significant advantages in SNR improvement. The\ncore of this scheme lies in the analysis and accurate reconstruction of\nthe waveform of Raman backscattered signals, which effectively\ncompensates for the detection signals distortion caused by the\ntransient effects of the system. This mechanism enables EAC-coding\nto overcome the performance bottleneck of traditional derived\nsequences coding schemes induced by signals distortion, achieving a\ncoding gain closer to the theoretical limit. Specifically, existing\nderived sequence coding scheme construct coding sequences based\non Golay complementary sequences and perform correlation\ndecoding using their derived sequences. The upper limit of their\ntheoretical coding gain is √L/2 (where L denotes the length of the\ncoding sequence). However, due to the unavoidable distortion\n(especially transient distortion) in actual detection signals, the results\nof their correlation operations deteriorate, leading to a significant gap\nbetween the actually achieved coding gain and this theoretical value.\nIn contrast, the EAC-coding scheme, through the aforementioned\nsignals analysis and reconstruction mechanism, significantly\nsuppresses the impact of transient distortion on the detection signals\nwaveform, thereby enabling its coding gain to approach the\ntheoretical upper limit of √L/2. Benefiting from this, the proposed\nsystem ultimately achieves temperature sensing capability in a long-\ndistance Raman distributed optical fiber sensing system with a\nsensing distance of 70.0 km.\nIn terms of measurement time, the core advantage of the EAC-\ncoding scheme stems from its extremely low decoding computational\ncomplexity. This scheme achieves signals reconstruction solely\nthrough Fourier transform, which significantly reduces the\ncomputational cost and time delay of real-time data processing,\nthereby effectively improving the overall response speed of the\nsystem. Specifically, for a Simplex code with length L, it is necessary\nto inject L groups of detection signals into the optical fiber and collect\nL groups of Raman backscattered signals, with its theoretical\nminimum acquisition time being TSimplex=L×t (where t denotes the\nacquisition time of one group of Raman backscattered curves).\nAlthough the Genetic-optimised aperiodic coding scheme only\nrequires injecting one group of detection signals into the optical fiber,\nit needs additional time to design the coding sequence based on the\ndistributed genetic algorithm. The Derived sequences coding scheme\nrequires injecting 4 groups of detection signals into the optical fiber,\nwith a theoretical acquisition time of 4t. However, in the decoding\nstage, it involves complex steps such as extracting the attenuation\nenvelope, establishing a compensation model, and solving the\ncompensation envelope via matrix operations, which increases the\ntime cost of the decoding process. The EAC-coding scheme proposed\nin this paper performs encoding based on Golay complementary\nsequences, with a theoretical acquisition time of 4t, and only needs\nFourier transform to complete the analysis and reconstruction of the\nRaman backscattered signals waveform. This significant efficiency\nimprovement at the algorithm level greatly reduces the real-time data\nprocessing delay and effectively enhances the system response speed,\nproviding crucial real-time guarantee for the final realization of\ntemperature sensing in a 70.0 km long-distance Raman distributed\noptical fiber sensing system.\nIn terms of system complexity, the core innovation of the EAC-\ncoding scheme lies in achieving a high degree of simplification in the\ndecoding process through algorithm optimization, while keeping the\nhardware architecture unchanged. This scheme only needs to perform\nefficient Fourier transform operations to complete signal\nreconstruction, which significantly reduces the algorithmic\ncomplexity and computational burden of real-time data processing.\nThe specific reasons are as follows. Simplex coding scheme requires\nthe injection of L groups of detection signals, resulting in a long\nacquisition time and a large volume of raw data. This not only\nimposes high requirements on hardware performance (such as data\nacquisition rate and storage capacity) and long-term stability, but also\nthe large-scale data processing involved in its decoding process\nsignificantly increases the computational complexity. Genetic-\noptimised aperiodic coding scheme greatly shortens the acquisition\ntime without increasing hardware costs. However, due to its unique\ndesign, it is necessary to design coding sequences based on a\ndistributed genetic algorithm and conduct extensive tests to find\nthe optimal coding sequence. Derived sequences coding scheme also\ndoes not require additional hardware overhead. However, this scheme\nintroduces high computational complexity in the decoding stage, as it\nrelies on computationally expensive matrix operations to generate and\nprocess derived sequences.\nEAC-coding scheme proposed in this paper incorporates a novel\npreprocessing framework for autocorrelation characteristic analysis,\nwaveform analysis and reconstruction of Raman backscattered\nsignals. This framework significantly improves the fidelity and\ntransmission stability of the encoded pulse sequence by dynamically\ncompensating for the transient gain fluctuation of EDFA. This\ntechnology leverages the inherent gain of EAC-coding pulse coding\nto effectively offset fiber scattering attenuation during 70.0 km long-\ndistance transmission, achieving a significant improvement in the\nbaseline SNR. On this basis, a two-stage noise suppression method is\nfurther constructed. The first-stage processing involves compensating\nfor signal attenuation using the theoretical coding gain of EAC-\ncoding. For the second-stage processing, a Haar wavelet denoising\nalgorithm is adopted. Its step-matching characteristic enables accurate\nextraction of the abrupt temperature change features of the sensing\nfiber and adaptive filtering of the residual time/frequency domain\ncoupled noise in the decoded signal. This three-fold synergistic\nmechanism, consisting of the preprocessing framework compensating\nfor EDFA fluctuation, coding gain suppressing transmission losses,\nand wavelet transform finely removing residual noise, breaks through\nthe theoretical trade-off bottleneck between SNR and sensing distance\nin traditional schemes. Experiment results indicate that, at an ultra-\nlong distance of 70.0 km, this scheme can achieve a spatial resolution\nof 1.58 m, a temperature resolution of 5.39 °C, and an effective\nnumber of sensing points reaching 44,303, verifying the engineering\nfeasibility of the scheme. To the best of our knowledge, the number\nof effective sensing points achieved by this scheme ranks the highest in\nthe field of Raman distributed optical fiber sensing systems.”\nResponds to the reviewers’ comments:\nReviewer 3 (Comments to the Author):\nRecommendations for the Author(s):\nThe response seems reasonable. Only remaining issue is the overhead in terms of the\ntime taken for the processing. Perhaps the authors can include that in the manuscript.\nReply: We sincerely appreciate your positive feedback and valuable\nsuggestion on our manuscript. Your recognition that our responses are reasonable\nis truly encouraging, and we are grateful for your thoughtful point regarding the\ntime costs—this is a critical aspect we will promptly address.\nFollowing your valuable suggestion, we will incorporate relevant content\nrelated to time costs into the manuscript, ensuring the information is clear,\ndetailed, and aligned with the study’s completeness. Details are as follows.\nThe current single measurement time is 252 minutes, limited by a pulse period\nof 700 μs and a number of averages of three million, with a theoretical\nmeasurement time of 35 min × 4 = 140 min. Due to the massive data volume\nexceeding the on-board real-time processing limit of the data acquisition card,\nthe measurement time is prolonged. In the future, a high-performance data acquisition\ncard will be upgraded and the data processing pipeline optimized, thereby\neliminating the delay degradation caused by hardware bottlenecks.\n1) In the section of Discussion, page 13, right column, paragraph 1,\nline 1, add “In terms of acquisition time cost, the current measurement time is\n252 minutes, limited by a pulse period of 700 μs and a number of averages\nof three million, with a theoretical measurement time of 35 min × 4 = 140\nmin. Due to the massive data volume exceeding the on-board real-time\nprocessing limit of the DAC, the measurement time is prolonged. In the\nfuture, a high-performance DAC will be upgraded and the data processing\npipeline optimized, thereby eliminating the delay degradation caused by\nhardware bottlenecks.”\nCorrections:\nWe would like to express our heartfelt thanks to all reviewers for the careful review\nof our manuscript and your valuable comments amid your busy schedules. The\nprofessional suggestions you provided have offered important guidance for improving\nthe quality of the manuscript, and we would like to extend our sincere gratitude for this.\nTo clearly present the full picture of revisions to the manuscript and facilitate the\nreviewers' verification of the implementation of these revisions, we have summarized\nall the revisions and supplements made based on the reviewers' comments.\nOnce again, we appreciate the attentive guidance from all reviewers.\nThank you for your suggestion. We have made the following modifications in\nour revised manuscript:\n1) In the section of Introduction, the following content has been relocated to the\nSupplementary Information. “Simplex coding scheme, as a linear coding technique\nbased on Hadamard matrix transformation, has its code length (in L bits)\ndetermining the number of detection signals required (L groups). For instance, in\n2006, J. Park, et al. achieved a spatial resolution of 17.0 m, a temperature resolution\nof 3.0 °C, and a total of 2176 effective sensing points over a sensing distance of\n37.0 km by utilizing this coding scheme and link optimization techniques. The main\nlimitation of this scheme lies in the linear growth of data acquisition volume and\ncomputational complexity with code length, which restricts its practical efficiency\nin applications requiring long code lengths and high-speed sensing.\nLow-repetition-rate cyclic pulse coding scheme generates Simplex coding-\nbased cyclic coding sequences using an acousto-optic modulator (AOM), enabling\npulses to be injected into the optical fiber periodically at a low repetition rate. For\nexample, in 2011, M. A. Soto, et al. combined the low-repetition-rate quasi-periodic\ncyclic pulse coding with a high-power fiber laser, achieving a spatial resolution of\n1.0 m, a temperature resolution of 3.0 °C, and 26,000 effective sensing points over\na sensing distance of 26.0 km. However, higher pulse energy also makes it more\nlikely to induce fiber nonlinear effects, and when approaching the stimulated\nscattering threshold, it restricts the system’s sensing distance and SNR performance.\nPre-Shaped Simplex Coding scheme is based on simplex coding technology\nand adopts a linearly increasing profile to adjust pulse amplitude, compensating for\nthe amplitude variation caused by EDFA to suppress the transient effect of the\nEDFA and improve system performance. For example, in 2017, J. B. Rosolem, et\nal. achieved a spatial resolution of 10.0 m, a temperature resolution of 8.4 °C, and\n6,200 effective sensing points over a sensing distance of 62.0 km by using the pre-\nshaped Simplex coding and a gain-controlled erbium-doped fiber amplifier.\nAlthough this scheme effectively suppresses the transient response of the EDFA at\nthe hardware level, its hardware structure is more complex, leading to a significant\nincrease in implementation cost.\nGenetic-optimised aperiodic coding scheme utilizes a distributed genetic\nalgorithm (DGA) to generate a single-sequence aperiodic code (GO-code), which\nis then converted into an optical pulse sequence and injected into the optical fiber.\nFor example, in 2020, X. Z. Sun, et al. achieved a spatial resolution of 1.0 m, a\ntemperature resolution of 3.9 °C, and 39,000 effective sensing points over a sensing\ndistance of 39.0 km based on the Genetic-optimised aperiodic coding scheme. The\ncore challenge of this scheme lies in its high dependence on optimization algorithms\nto search for the optimal code, which typically requires substantial computational\nresources and iterative testing.\nDerived Sequences coding scheme addresses the transient effects of EDFA\nthrough a derived sequence decoding method, thereby enhancing the performance\nof long-distance sensing. For instance, in 2022, D. D. Chai, et al. achieved a spatial\nresolution of 5.0 m, a temperature resolution of 2.5 °C, and 8,800 effective sensing\npoints over a sensing distance of 44.0 km based on the Derived Sequences coding\nscheme. However, this scheme’s decoding process imposes a heavy computational\nburden, and the core algorithm involves high-complexity matrix operations, making\nit difficult to meet real-time requirements.”\n2) In the section of Discussion, the following content has been relocated to the\nSupplementary Information. “Currently, the pulse coding techniques applied in\nRaman distributed optical fiber sensing system mainly include the following:\nSimplex coding scheme, Pre-Shaped Simplex coding scheme, Low-repetition-rate\ncyclic pulse coding scheme, Genetic-optimised aperiodic coding scheme, and\nDerived Sequences coding scheme. Their key performance indicators are presented\nin Table 2.\nWe have compared our proposed scheme with other coding methods such as\nsimplex coding and Genetic-optimised aperiodic coding in terms of coding gain,\nmeasurement time, and system complexity. The specific revisions are as follows.\nIn terms of coding gain, the EAC-coding scheme proposed in this paper\nexhibits significant advantages in SNR improvement. The core of this scheme lies\nin the analysis and accurate reconstruction of the waveform of Raman backscattered\nsignals, which effectively compensates for the detection signals distortion caused\nby the transient effects of the system. This mechanism enables EAC-coding to\novercome the performance bottleneck of traditional derived sequences coding\nschemes induced by signals distortion, achieving a coding gain closer to the\ntheoretical limit. Specifically, existing derived sequence coding scheme construct\ncoding sequences based on Golay complementary sequences and perform correlation\ndecoding using their derived sequences. The upper limit of their theoretical coding\ngain is √L/2 (where L denotes the length of the coding sequence). However, due to\nthe unavoidable distortion (especially transient distortion) in actual detection\nsignals, the results of their correlation operations deteriorate, leading to a\nsignificant gap between the actually achieved coding gain and this theoretical value.\nIn contrast, the EAC-coding scheme, through the aforementioned signals analysis\nand reconstruction mechanism, significantly suppresses the impact of transient\ndistortion on the detection signals waveform, thereby enabling its coding gain to\napproach the theoretical upper limit of √L/2. Benefiting from this, the proposed\nsystem ultimately achieves temperature sensing capability in a long-distance\nRaman distributed optical fiber sensing system with a sensing distance of 70.0 km.\nIn terms of measurement time, the core advantage of the EAC-coding scheme\nstems from its extremely low decoding computational complexity. This scheme\nachieves signals reconstruction solely through Fourier transform, which\nsignificantly reduces the computational cost and time delay of real-time data\nprocessing, thereby effectively improving the overall response speed of the system.\nSpecifically, for a Simplex code with length L, it is necessary to inject L groups of\ndetection signals into the optical fiber and collect L groups of Raman backscattered\nsignals, with its theoretical minimum acquisition time being TSimplex=L×t (where\nt denotes the acquisition time of one group of Raman backscattered curves).\nAlthough the Genetic-optimised aperiodic coding scheme only requires injecting\none group of detection signals into the optical fiber, it needs additional time to\ndesign the coding sequence based on the distributed genetic algorithm. The Derived\nsequences coding scheme requires injecting 4 groups of detection signals into the\noptical fiber, with a theoretical acquisition time of 4t. However, in the decoding\nstage, it involves complex steps such as extracting the attenuation envelope,\nestablishing a compensation model, and solving the compensation envelope via\nmatrix operations, which increases the time cost of the decoding process. The EAC-\ncoding scheme proposed in this paper performs encoding based on Golay\ncomplementary sequences, with a theoretical acquisition time of 4t, and only needs\nFourier transform to complete the analysis and reconstruction of the Raman\nbackscattered signals waveform. This significant efficiency improvement at the\nalgorithm level greatly reduces the real-time data processing delay and effectively\nenhances the system response speed, providing crucial real-time guarantee for the\nfinal realization of temperature sensing in a 70.0 km long-distance Raman\ndistributed optical fiber sensing system.\nIn terms of system complexity, the core innovation of the EAC-coding scheme\nlies in achieving a high degree of simplification in the decoding process through\nalgorithm optimization, while keeping the hardware architecture unchanged. This\nscheme only needs to perform efficient Fourier transform operations to complete\nsignal reconstruction, which significantly reduces the algorithmic complexity and\ncomputational burden of real-time data processing. The specific reasons are as\nfollows. Simplex coding scheme requires the injection of L groups of detection\nsignals, resulting in a long acquisition time and a large volume of raw data. This not\nonly imposes high requirements on hardware performance (such as data acquisition\nrate and storage capacity) and long-term stability, but also the large-scale data\nprocessing involved in its decoding process significantly increases the\ncomputational complexity. Genetic-optimised aperiodic coding scheme greatly\nshortens the acquisition time without increasing hardware costs. However, due to\nits unique design, it is necessary to design coding sequences based on a distributed\ngenetic algorithm and conduct extensive tests to find the optimal coding sequence.\nDerived sequences coding scheme also does not require additional hardware\noverhead. However, this scheme introduces high computational complexity in the\ndecoding stage, as it relies on computationally expensive matrix operations to\ngenerate and process derived sequences.\nEAC-coding scheme proposed in this paper incorporates a novel preprocessing\nframework for autocorrelation characteristic analysis, waveform analysis and\nreconstruction of Raman backscattered signals. This framework significantly\nimproves the fidelity and transmission stability of the encoded pulse sequence by\ndynamically compensating for the transient gain fluctuation of EDFA. This\ntechnology leverages the inherent gain of EAC-coding pulse coding to effectively\noffset fiber scattering attenuation during 70.0 km long-distance transmission,\nachieving a significant improvement in the baseline SNR. On this basis, a two-stage\nnoise suppression method is further constructed. The first-stage processing involves\ncompensating for signal attenuation using the theoretical coding gain of EAC-\ncoding. For the second-stage processing, a Haar wavelet denoising algorithm is\nadopted. Its step-matching characteristic enables accurate extraction of the abrupt\ntemperature change features of the sensing fiber and adaptive filtering of the\nresidual time/frequency domain coupled noise in the decoded signal. This\nthree-fold synergistic mechanism, consisting of the preprocessing framework\ncompensating for EDFA fluctuation, coding gain suppressing transmission losses,\nand wavelet transform finely removing residual noise, breaks through the\ntheoretical trade-off bottleneck between SNR and sensing distance in traditional\nschemes. Experiment results indicate that, at an ultra-long distance of 70.0 km,\nthis scheme can achieve a spatial resolution of 1.58 m, a temperature resolution of\n5.39 °C, and an effective number of sensing points reaching 44,303, verifying the\nengineering feasibility of the scheme. To the best of our knowledge, the number of\neffective sensing points achieved by this scheme ranks the highest in the field of\nRaman distributed optical fiber sensing systems.”"}]

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