Improving the Thresholds of Generalized LDPC Codes with Convolutional Code Constraints

TL;DR

This paper investigates how introducing irregularity in convolutional code constraints within CC-GLDPC codes can significantly improve BP decoding thresholds on the BEC, with minor effects on MAP thresholds, supported by simulations on AWGN channels.

Contribution

It extends CC-GLDPC codes by adding irregularity at constraint nodes and analyzes their impact on decoding thresholds, providing a comprehensive comparison with regular ensembles.

Findings

Irregularity improves BP thresholds significantly.

MAP thresholds are only slightly affected by irregularity.

Simulation results align with threshold improvements.

Abstract

CC-GLPDC codes are a class of generalized low-density parity-check (GLDPC) codes where the constraint nodes (CNs) represent convolutional codes. This allows for efficient decoding in the trellis with the forward-backward algorithm, and the strength of the component codes easily can be controlled by the encoder memory without changing the graph structure. In this letter, we extend the class of CC-GLDPC codes by introducing different types of irregularity at the CNs and investigating their effect on the BP and MAP decoding thresholds for the binary erasure channel (BEC). For the considered class of codes, an exhaustive grid search is performed to find the BP-optimized and MAP-optimized ensembles and compare their thresholds with the regular ensemble of the same design rate. The results show that irregularity can significantly improve the BP thresholds, whereas the thresholds of the MAP-optimized ensembles are only slightly different from the regular ensembles. Simulation results for the AWGN channel are presented as well and compared to the corresponding thresholds.