## 1 Introduction  
Underwater acoustic channels are complex and variable [1; 2; 3], and spread-spectrum communication techniques [4; 5; 6] are often used for robust acoustic communication. Considering the low-latency requirements of the communication system and the frame data volume of underwater acoustic spread-spectrum systems, short-block-length code is generally preferable in terms of its decoding latency and short-frame-data transmission. [PERSON] et al. constructed a quasi-cyclic LDPC (QC-LDPC) code based on Euclidean geometry and cyclic decomposition, which has a shorter girth, and, by comparing the BER performance of LDPC codes based on the randomized construction method with those constructed based on this method under different modulation modes, the (256,128) code based on the design of the method has a good performance [7]. [PERSON] et al. proposed a new method for constructing LDPC codes based on the Orange Book of the Consultative Committee on Space Data Systems (CCSDS), \"Short Block Length LDPC Codes for TC Synchronization and Channel Coding\", and the simulation experiments show that, compared with the LDPC codes in the experimental specification, the LDPC code constructed using this method can obtain about a 0.4 dB gain when the SER is 1 \(\times 10^{-7}\)[8]. [PERSON] et al. proposed a protograph-based Raptor-like (PBRL) low-density parity-check code design method that can obtain a better error frame rate at short-code-block lengths [9]. [PERSON] et al. constructed short-block LDPC codes using an improved progressive edge-growth (PEG) algorithm; the LDPC codes constructed by this method have a shorter girth with a better approximate cycle extrinsic message degree than the existing PEG algorithm [10]. For spread-spectrum coding systems, in 2020, [PERSON] et al. [11] applied coding techniques to an ultrawideband spread-spectrum system and compared the performance of the spread-spectrum system using Turbo [12; 13; 14], low-density parity check (LDPC) [15; 16] and Polar codes [17; 18; 19]. The direct sequence spread spectrum (DSSS) with a bit error rate (BER) of \(10^{-4}\) and a bandwidth of 1.2 GHz provided a spread-spectrum gain of about 21 dB. The spread-spectrum system using LDPC codes achieved a combined gain of over 30 dB, allowing for the successful retrieval of message signals with \(1000\times\) higher power interference. [PERSON] et al. applied spread-spectrum coding techniques to UV scattering communication systems. Using the direct spread-spectrum method and LDPC codes with a code rate of \(1/2\) and a code length of 1024, the results showed that the coded system could achieve a BER of \(10^{-2}\) at \(-2\) dB, while the non-coded system achieved a BER of \(10^{-1}\)[20]. [PERSON] et al. combined QC-LDPC code with spread-spectrum technology and high-order modulation technology, and the performance of an underwater acoustic spread-spectrum communication system is investigated: through simulation experiments, the underwater acoustic spread-spectrum system combining LDPC code has a better performance compared with the spread-spectrum system combining Turbo code, and can obtain a better BER performance under a low signal-to-noise ratio [21]. For spread-spectrum systems in underwater acoustics communications, in 2021, [PERSON] et al. addressed the signal distortion problem caused by the Doppler effect in mobile underwater acoustic communication scenarios by using different spread-spectrum codes with different frequency offsets as local reference signals, correlating the received signals one by one and searching for the maximum correlation value in the frequency domain and the code domain in order to complete the signal descaling and Doppler estimation. Simulations and experiments show that, compared to the average Doppler-compensated sliding correlation spread-spectrum method, this method has a better BER performance [5]. [PERSON] et al.