Hamming-GLDPC codes in BEC and AWGN channel

Hamming codes are used as component codes to construct generalized low-density parity-check (GLDPC) codes. In BEC channel, the convergence behavior of the Hamming-GLDPC codes is theoretically analyzed with EXIT chart. The duality property of Hamming codes and simplex codes helps to get the EXIT chart of Hamming code with the bridge of the EXIT of simplex codes. The analysis shows that the advantage of convergence for Hamming-GLDPC codes is obvious over the duplicate standard LDPC codes. In AWGN channel, simulation results of the GLDPC code with Hamming (7, 4) code as component code also indicate the powerful decoding performance of Hamming-GLDPC codes. Up to 1.5 dB coding gain can be obtained for GLDPC code in comparison with the counterpart standard LDPC code at BER of 10^-3.