Hybrid hamming GLDPC codes over the binary erasure channel

Abstract

Generalized low-density parity-check (GLDPC) codes are a class of iteratively decodable codes, which can change code rate flexibly and be close to the Shannon limit. Empirical evidence suggests that GLDPC codes have advantages over standard low-density parity-check (LDPC) codes in both of error floor and waterfall performance. In this paper, to further approach Shannon limit, the strategy of mixing single parity check (SPC) code with Hamming code to act as the component code of the check nodes (CNs) for GLDPC code is proposed. By using extrinsic information transfer (EXIT) chart, we can estimate the decoding threshold and degree distribution through adjusting the proportion of SPC code and Hamming code over the binary erasure channel (BEC). With the aid of EXIT charts, we construct GLDPC code based on the best degree distribution. Simulation results show that, in comparison with standard LDPC codes and the state-of-the-art GLDPC codes with hybrid variable nodes (VNs), the GLDPC code proposed in this paper has better asymptotic performance.