Nested Array-Based Spatially Coupled LDPC Codes

TL;DR

This paper introduces a multi-step optimization method for nested array-based spatially coupled LDPC codes to reduce harmful absorbing sets, enhancing high-SNR performance, with the order of optimization significantly affecting outcomes.

Contribution

It proposes a line-counting based optimization scheme for nested SC-LDPC codes, addressing constraints due to overlapping sub-codes and demonstrating improved elimination of absorbing sets.

Findings

Optimization order affects the number of absorbing sets.

Complete removal of dominant absorbing sets is achievable for certain parameters.

Tradeoff exists between code performance and optimization sequence.

Abstract

Linear nested codes, where two or more sub-codes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled low-density parity-check (SC-LDPC) codes and propose a line-counting based optimization scheme for minimizing the number of dominant absorbing sets in order to improve its performance in the high signal-to-noise ratio regime. Since the parity-check matrices of different nested sub-codes partially overlap, the optimization of one nested sub-code imposes constraints on the optimization of the other sub-codes. To tackle these constraints, a multi-step optimization process is applied first to one of the nested codes, then sequential optimization of the remaining nested codes is carried out based on the constraints imposed by the previously optimized sub-codes. Results show that the order of optimization has a significant impact on the number of dominant absorbing sets in the Tanner graph of the code, resulting in a tradeoff between the performance of a nested code structure and its optimization sequence: the code which is optimized without constraints has fewer harmful structures than the code which is optimized with constraints. We also show that for certain code parameters, dominant absorbing sets in the Tanner graphs of all nested codes are completely removed using our proposed optimization strategy.