更新式の近似に基づく Low-Density Parity-Check 符号簡易復号法の検討

塁 阪井, 松本 渉, 英夫 吉田

Chang, Dongxu, Qingqing Peng, Ma, Zhiming +2 more

In this study, the performance of generalized low-density parity-check (GLDPC) codes under the a posteriori probability (APP) decoder is analyzed. We explore the concentration, symmetry, and monotonicity properties of GLDPC codes under the APP decoder, extending the applicability of density evolution to GLDPC codes. On the binary memoryless symmetric channels, using the BEC and BI-AWGN channels as two examples, we demonstrate that with an appropriate proportion of generalized constraint (GC) nodes, GLDPC codes can reduce the original gap to capacity compared to their original LDPC counterparts. Additionally, on the BI-AWGN channel, we apply and improve the Gaussian approximation algorithm in the density evolution of GLDPC codes. By adopting Gaussian mixture distributions to approximate the message distributions from variable nodes and Gaussian distributions for those from constraint nodes, the precision of the channel parameter threshold can be significantly enhanced while maintaining a low computational complexity similar to that of Gaussian approximations. Furthermore, we identify a class of subcodes that can greatly simplify the performance analysis and practical decoding of GLDPC codes, which we refer to as message-invariant subcodes. Using the aforementioned techniques, our simulation experiments provide empirical evidence that GLDPC codes, when decoded with the APP decoder and equipped with the right fraction of GC nodes, can achieve substantial performance improvements compared to low-density parity-check (LDPC) codes.

S. Hirst, B. Honary

A generalised low-density parity-check code (GLDPC) is a low-density parity-check code in which the constraint nodes of the code's graph are replaced with component or subcodes other than single parity checks. Gallager's bit-flipping algorithm for LDPCs is generalised to the class of GLDPCs with Hamming subcodes. The proposed weighted bit-flip voting (WBFV) method is iterative and uses only the hard decision decoder of the Hamming subcodes. Decoding of Hamming-based GLDPCs using WBFV has been simulated on the binary symmetric channel. Simulation results are presented showing the variation in performance with voting rule, graph construction and block length. In terms of the dependence of coding gains and complexity on the GLDPC block length, the proposed method is found to display a good performance to decoding complexity trade-off. Performance is found to compete well with other more conventional hard decision decoding schemes.

塁 阪井, 渉 松本, 英夫 吉田

Marco Baldi

Jie Xu, Zhiyong Zheng, Kun Tian

In this paper, we conclude five kinds of methods for construction of the regular low-density parity matrix H and three kinds of methods for the construction of irregular low-density parity-check matrix H. Through the analysis of the code rate and parameters of these eight kinds of structures, we find that the construction of low-density parity-check matrix tends to be more flexible and the parameter variability is enhanced. We propose that the current development cost should be lower with the progress of electronic technology and we need research on more practical Low-Density Parity-Check Codes (LDPC). Combined with the application of the quantum distribution key, we urgently need to explore the research direction of relevant theories and technologies of LDPC codes in other fields of quantum information in the future.