A Generalized Algebraic Approach to Optimizing SC-LDPC Codes

摘要

Spatially coupled low-density parity-check (SC-LDPC) codes are sparse graphcodes that have recently become of interest due to their capacity-approachingperformance on memoryless binary input channels. In this paper, we unify allexisting SC-LDPC code construction methods under a new generalized descriptionof SC-LDPC codes based on algebraic lifts of graphs. We present an improvedlow-complexity counting method for the special case of $(3,3)$-absorbing setsfor array-based SC-LDPC codes, which we then use to optimize permutationassignments in SC-LDPC code construction. We show that codes constructed inthis way are able to outperform previously published constructions, in terms ofthe number of dominant absorbing sets and with respect to both standard andwindowed decoding.