Design of Efficiently Encodable Moderate-Length High-Rate Irregular LDPC Codes

TLDR

This paper introduces a new class of irregular low‑density parity‑check codes with moderate length (10^3–10^4) and high rate (3/4). The design algorithm combines density evolution and differential evolution optimization with a modified cost function, and the scheme is applicable to irregular LDPC codes of various lengths and rates. These codes achieve low‑complexity encoding, lower error‑rate floors than other irregular LDPC designs, equivalence to systematic serial turbo codes and an extension of irregular repeat‑accumulate codes, and exhibit no error‑rate floors down to a bit‑error rate of 10^-9.

Abstract

This paper presents a new class of irregular low-density parity-check (LDPC) codes of moderate length (10/sup 3//spl les/n/spl les/10/sup 4/) and high rate (R/spl ges/3/4). Codes in this class admit low-complexity encoding and have lower error-rate floors than other irregular LDPC code-design approaches. It is also shown that this class of LDPC codes is equivalent to a class of systematic serial turbo codes and is an extension of irregular repeat-accumulate codes. A code design algorithm based on the combination of density evolution and differential evolution optimization with a modified cost function is presented. Moderate-length, high-rate codes with no error-rate floors down to a bit-error rate of 10/sup -9/ are presented. Although our focus is on moderate-length, high-rate codes, the proposed coding scheme is applicable to irregular LDPC codes with other lengths and rates.