Research and Application of Several Error Correction Codes in Communication

Abstract

Error correction code is an important part of contemporary communication engineering, first proposed by Shannon, and has become mature nowadays. This paper analyzes and compares the error correction capabilities of BCH code, cyclic code, and Hamming code using BPSK modulation in AWGN channels. It unfolds in chronological order, introducing the popular codewords of various eras of the last century in turn. Moreover, it introduces the communication process of BPSK modulation and its addition of three codes and compares the bit error rates of the output signals of them when the input signal is a Bernoulli binary sequence. After simulation, it is found that there is a strong correlation between the number of bit errors in BPSK modulation and the code used and its length At low SNR (signal-to-noise ratio),the error rate error of using codewords or not is minimal. Most digital devices exhibit advantages when the SNR exceeds 4 dB. Under the equivalent SNR, the longer the codeword, the lower the error rate, and the best error correction ability of BCH code (31,11,5). This article only discusses the error correction ability of BPSK under modulation, laying a foundation for comparing the error correction ability of higher order PSK modulation and other code words in the future.