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

TL;DR

This paper introduces a linear programming-based method for designing irregular spatially-coupled LDPC codes with non-uniform degree distributions, improving their performance over regular codes.

Contribution

It presents a novel low-complexity design approach for irregular SC-LDPC codes using local degree distribution design and pre-computation techniques.

Findings

Designed codes outperform regular SC-LDPC codes in asymptotic performance.

Proposed method reduces complexity of code design.

Irregular codes show superior finite-length performance.

Abstract

In this paper, we propose a new design method of irregular spatially-coupled low-density parity-check (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 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 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.