Doubly Generalized LDPC Codes over the AWGN Channel

In this paper, the design of doubly generalized low-density parity-check (DGLDPC) codes is proposed. This approach generalizes the structure of LDPC codes at both check and variable nodes. The performance of DGLDPC codes over the AWGN channel is analyzed using EXIT charts. Combined with differential evolution optimization, this analysis provides thresholds for DGLDPC codes that are better than that of LDPC and GLDPC codes with the same maximum variable degree. These theoretical thresholds are verified via simulations. Furthermore DGLDPC codes exhibit a lower error floor compared with their LDPC and GLDPC counterparts.