Close-to-capacity performance of extended single parity check product codes

The empirical performances of extended single parity check product codes, which are very simple and of low complexity, on a binary input additive white Gaussian noise channel by a belief propagation (BP) decoding algorithm, are presented. Simulation results show that the codes can achieve close-to-capacity performance in high code rate. The codes approach the Shannon limit according to the increase of the code length. The code of length 97751 and of rate 0.985 is only 0.44 dB away from the Shannon limit for a BER of 10^-5.