# Polar Codes and a M-ary Modulation-Based OFDM-PLC System
###### Abstract  
Power Line Communication (PLC) serves as a medium for communication over power lines, utilizing the existing power grid for information transmission. It offers a low-cost, highly scalable signal transmission method and has the potential to become the preferred technology for providing broadband in smart homes, offices, and smart grids. However, noise in the power line channel, especially impulse noise, seriously affects the communication quality of PLC. In this paper, we establish an OFDM-PLC system with higher-order modulation and polar codes. The higher-order QAM or APSK modulation technique is employed to increase the signal transmission rate and the system performance is analyzed. To combat the impulse noise in the PLC channel, we first model it using a superposition of multi-damping sinusoidal functions and then introduce the polar coding scheme to suppress the impulse noise in the system, thereby improving the transmission reliability. Simulation results verify that the proposed polar coding scheme based on the OFDM-PLC system can improve the Bit Error Rate (BER) performance of PLC channel transmission under impulse interference. P 2023 2  
To characterize the characteristics of various types of noise, the Middleton-A model is the most popular non-Gaussian noise model, which is composed of narrowband impulse noise and Gaussian noise. Many researchers use this type of noise model when studying PLC channels [11]. However, Middleton-A class noise, as a human-made impulse construction method, is composed of independent sampling points, which cannot reproduce the physical characteristics of impulse noise oscillation attenuation, and therefore needs further improvement. On the other hand, with the continuous development of modern digital signal processing technologies such as modulation and channel coding, Orthogonal Frequency Division Multiplexing (OFDM) technology is considered to be an effective method for solving problems such as noise, multipath propagation, and frequency-selective fading in PLC [12]. In [13], the performance of using OFDM in PLC channels was analyzed and compared with single-carrier modulation systems, and the authors pointed out that OFDM outperformed single-carrier modulation in terms of BER performance. For channel coding, the authors in [14] proved that modeled PLC channels can have good image transmission capabilities with the help of LDPC coding. In [15], the authors compared the performance of LDPC codes and Turbo codes in the PLC environment and proved that the performance of LDPC codes can approach that of Turbo codes with higher block lengths. In [16], OFDM technology with subcarrier mapping using BPSK and QAM achieved excellent performance by introducing LDPC codes in error correction coding. Recently, after [PERSON] et al. invented polar codes [17], many studies have shown that polar codes can achieve good performance when applied to PLC systems with impulse noise. [PERSON] et al. [18] evaluated the BER performance of polar codes against impulse noise, but only in single-carrier scenarios. Furthermore, they solved the problem of limited single-carrier scenarios in [18] by introducing polar coding in OFDM-based multi-carrier PLC systems and discussing Successive Cancellation (SC) decoding techniques [19]. Based on this, two decoding methods, Successive Cancellation List (SCL) and Successive Cancellation Stack (SCS), were proposed to improve the performance of polar codes. In addition, [PERSON] et al. [20] pointed out that soft decision decoding is superior to hard decision decoding, and performance can be further improved with increasing code word length. They also proved that polar codes have stronger capabilities than other codes in correcting errors caused by impulse noise in PLC systems. In this paper, we propose an OFDM-PLC system with higher-order modulation and polar encoding modules under impulse noise. In order to describe the impulse noise more accurately, a multi-damping sinusoidal function is used to model the impulse noise in the PLC channel.