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.