(7, 4)-Hamming generalized LDPC code for Rayleigh fading channel

To get a generalized version of LDPC code, we construct (7, 4)-Hamming GLDPC code with (7, 4) Hamming component code in this paper, and give the number of short cycles of this GLDPC code as well as the code weight distribution. Via MLD, the negative effects of short cycles limited in the Hamming block can be eliminated. Simulation results show that, up to 2 dB coding gain can be obtained for GLDPC code, with faster convergence rate, in comparison with the counterpart standard code, at BER of 10−7 in Rayleigh fading channel. Even compared with the standard LDPC code which has no 4-cycles, the better behaviors for GLDPC code, with still faster convergence rate, are achieved in several limits. These results may enhance the implementation of this GLDPC code in real world.