A Generalized Algebraic Approach to Optimizing SC-LDPC Codes

TL;DR

This paper introduces a unified algebraic framework for constructing SC-LDPC codes, enabling optimization of code properties and outperforming previous designs in reducing absorbing sets and improving decoding performance.

Contribution

It presents a generalized algebraic approach to SC-LDPC code construction and an efficient method for optimizing permutation assignments to enhance code performance.

Findings

Optimized codes have fewer dominant absorbing sets.

Constructed codes outperform previous designs in decoding performance.

The algebraic framework unifies existing SC-LDPC construction methods.

Abstract

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