An Ensemble of Iteratively Decodable Codes Constructed Based on a Superposition Method

Abstract

In this paper, the construction of new families of error-correcting codes adapted from Boutros and Lentmaier's generalized low-density (GLD) codes, which we called generalized irregular low-density (GILD) codes, is investigated. By introducing irregular base matrices, significant improvements on Boutros and Lentmaier's results are achieved. Two cases are considered; in the first case, the same constituent code is used, and in the second case, different constituent codes are used. It is proved by an ensemble performance argument that these codes exist and are asymptotically good in the sense of the minimum-distance criterion. It is also proved that the performance of GILD codes approaches the binary symmetric channel capacity limit. Iterative decoding of GILD codes for communication over an additive white Gaussian noise channel is also studied. The high flexibility in selecting the parameters of GILD codes and their better performance and higher rate make them more attractive than GLD codes, and hence, suitable for small and medium block lengths forward-error-correcting schemes. Comparisons of simulation results between some GILD codes and some good low-density parity-check codes show very close performances