Controlling LDPC Absorbing Sets Via the Null Space of the Cycle Consistency Matrix

This paper focuses on controlling absorbing sets 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 and include array-based LDPC codes and many common quasi-cyclic codes. SCB codes retain standard properties of quasi-cyclic LDPC codes such as girth, code structure, and compatibility with existing high-throughput hardware implementations. This paper uses 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.