Design of Irregular SC-LDPC Codes With Non-Uniform Degree Distributions by Linear Programing.

In this paper, we propose a new design method of irregular spatially-coupledlow-density paritycheck (SC-LDPC) codes with non-uniform degree distributionsby linear programming (LP). In general, irregular SC-LDPC codes withnon-uniform degree distributions is difficult to design with low complexitybecause their density evolution equations are multi-dimensional. To solve theproblem, the proposed method is based on two main ideas: a local design of thedegree distributions for each pair of positions and pre-computation of theinput/output message relationship. These ideas make it possible to design thedegree distributions of irregular SC-LDPC codes by solving low complexity LPproblems which are used when optimizing uncoupled low-density parity-check(LDPC) codes over the binary erasure channel. We also find a proper objectivefunction for the proposed design methodology to improve the performance ofSC-LDPC codes. It is shown that the irregular SC-LDPC codes obtained by theproposed method are superior to regular SC-LDPC codes in terms of bothasymptotic and finite-length performances.