Design and performance evaluation of some high-rate irregular low-density parity-check codes

The irregular low-density parity-check codes (LDPCC) have been proposed by Richardson, Shokrollahi and Urbanke (see IEEE Trans. on Inf. Theory), in many cases outperforming the best known turbo-codes. These results have been obtained by allowing the degree of nodes (variable or check) of a LDPCC to vary according to some distribution. We give new distributions to design high rate irregular LDPCC, more precisely rates 7/8, 8/9 and 15/16, motivated by applications to space data communication. Then, we investigate the performance of these new codes over AWGN channels, for different codeword lengths. The error rates obtained are always less than 1 dB from the channel capacity, and in most cases better than the results obtained by turbo-codes with the same parameters. Finally, we investigate, by means of an original method, the minimum distance of irregular LDPCC. The results show that irregular LDPCC have quite low minimum distance, giving rise, similarly to turbo-codes, to the "error floor" phenomenon.