Design of Irregular SC-LDPC Codes With Non-Uniform Degree Distributions by Linear Programing
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In this paper, we propose a new design method of irregular spatially-coupled low-density paritycheck (SC-LDPC) codes with non-uniform degree distributions by linear programming (LP). In general, irregular SC-LDPC codes with non-uniform degree distributions is difficult to design with low complexity because their density evolution equations are multi-dimensional. To solve the problem, the proposed method is based on two main ideas: a local design of the degree distributions for each pair of positions and pre-computation of the input/output message relationship. These ideas make it possible to design the degree distributions of irregular SC-LDPC codes by solving low complexity LP problems which are used when optimizing uncoupled low-density parity-check (LDPC) codes over the binary erasure channel. We also find a proper objective function for the proposed design methodology to improve the performance of SC-LDPC codes. It is shown that the irregular SC-LDPC codes obtained by the proposed method are superior to regular SC-LDPC codes in terms of both asymptotic and finite-length performances.
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