纠正随机错误与长突发删除的多进制乘积码研究

考虑多进制LDPC码的符号特性,以及对其残留错误和删除的分析,本文采用多进制LDPC码作为内码,相同Galois域下的高码率RS码作为外码来构造多进制乘积码;并提出了一种低复杂度的迭代译码方案,减少信息传输的各类错误。在译码时,只对前一次迭代中译码失败的码字执行译码,并对译码正确码字所对应的比特初始概率信息进行修正,增强下一次迭代多进制LDPC译码符号先验信息的准确性,减少内码译码后的判决错误,从而充分利用外码的纠错能力。仿真结果显示,多进制乘积码相较于二进制LDPC乘积码有较大的编码增益,并通过迭代进一步改善了性能,高效纠正了信道中的随机错误和突发删除。对于包含2%突发删除的高斯信道,在误比特率为10^-6时,迭代一次有0.4 dB左右的增益。

Research on Non-Binary Product Codes for Correcting Random Errors with Long Burst Erasures

Considering the symbol characteristic of non-binary LDPC code, this paper used the non-binary LDPC code as the inner code, the high rate RS code under the same Galois field as the outer code to construct the non-binary product code based on the analysis of the residual erasures and errors; and a novel iterative method for non-binary product code is proposed to further reduce the various errors in information transmission. During the iterative decoding, only codewords that failed to decode in the previous iteration are performed decoding, and the corresponding bit probability of the corrected codeword is modified to enhance the prior information accuracy of symbol in non-binary LDPC decoding of next iteration. Then, the decision error after inner decoding is decreased, and thereby the error correction capability of the outer code can be full exploited. Simulation results show that the proposed non-binary product code scheme had excellent coding gain compared with binary LDPC product code, the performance was further improved using iteration, and the random errors and long burst erasures were effectively corrected. For AWGN channel with 2% erasures, 0.4 dB gain can be obtained through iteration when the bit error rate is 10-6.