Absorbing Set Spectrum Approach for Practical Code Design

TL;DR

This paper introduces a novel method using cycle consistency matrices to systematically eliminate absorbing sets in SCB LDPC codes, leading to improved error-floor performance.

Contribution

It develops a CCM-based approach for designing SCB LDPC codes that avoid dominant absorbing sets, enhancing low-error-rate performance.

Findings

Designed codes show steeper error-floor slope

Achieved at least tenfold improvement in low error rate region

Method effectively eliminates specific absorbing sets

Abstract

This paper focuses on controlling the absorbing set spectrum for a class of regular LDPC codes known as separable, circulant-based (SCB) codes. For a specified circulant matrix, SCB codes all share a common mother matrix, examples of which are array-based LDPC codes and many common quasi-cyclic codes. SCB codes retain the standard properties of quasi-cyclic LDPC codes such as girth, code structure, and compatibility with efficient decoder implementations. In this paper, we define a cycle consistency matrix (CCM) for each absorbing set of interest in an SCB LDPC code. For an absorbing set to be present in an SCB LDPC code, the associated CCM must not be full columnrank. Our approach selects rows and columns from the SCB mother matrix to systematically eliminate dominant absorbing sets by forcing the associated CCMs to be full column-rank. We use the CCM approach to select rows from the SCB mother matrix to design SCB codes of column weight 5 that avoid all low-weight absorbing sets (4, 8), (5, 9), and (6, 8). Simulation results demonstrate that the newly designed code has a steeper error-floor slope and provides at least one order of magnitude of improvement in the low error rate region as compared to an elementary array-based code.