Absorbing Set Spectrum Approach for Practical Code Design
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, the authors 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 column-rank.