The Cycle Consistency Matrix Approach to Absorbing Sets in Separable Circulant-Based LDPC Codes
For Low-Density Parity-Check (LDPC) codes operating over additive white Gaussian noise channels and decoded using message-passing decoders with limited precision, absorbing sets have been shown to be a key factor in error floor behavior. Focusing on this scenario, this paper introduces the Cycle Consistency Matrix (CCM) as a powerful analytical tool for characterizing and avoiding absorbing sets in Separable Circulant-Based (SCB) LDPC codes. SCB codes include a wide variety of regular LDPC codes such as array-based LDPC codes as well as many common quasi-cyclic codes. As a consequence of its cycle structure, each potential absorbing set in an SCB LDPC code has a CCM, and an absorbing set can be present in an SCB LDPC code only if the associated CCM has a nontrivial null space.