Spatially Coupled Generalized LDPC Codes: Asymptotic Analysis and Finite Length Scaling

TL;DR

This paper provides a comprehensive analysis of spatially coupled generalized LDPC codes, including their decoding thresholds, asymptotic distance properties, and finite-length scaling behavior, demonstrating their capacity-approaching performance and asymptotic goodness.

Contribution

It introduces a detailed analysis of SC-GLDPC codes, including threshold saturation, asymptotic distance properties, and finite-length scaling, advancing understanding of their performance and potential advantages.

Findings

Threshold saturation effect enables capacity approaching decoding thresholds.

SC-GLDPC ensembles are asymptotically good with favorable distance properties.

Finite-length scaling analysis shows performance benefits over traditional GLDPC codes.

Abstract

Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result in improved error floor performance, due to better minimum distance and trapping set properties, at a cost of some increased decoding complexity. In this paper, we study spatially coupled generalized low-density parity-check (SC-GLDPC) codes and present a comprehensive analysis of these codes, including: (1) an iterative decoding threshold analysis of SC-GLDPC code ensembles demonstrating capacity approaching thresholds via the threshold saturation effect; (2) an asymptotic analysis of the minimum distance and free distance properties of SC-GLDPC code ensembles, demonstrating that the ensembles are asymptotically good; and (3) an analysis of the finite-length scaling behavior of both GLDPC block codes and SC-GLDPC codes based on a peeling decoder (PD) operating on a binary erasure channel (BEC). Results are compared to GLDPC block codes, and the advantages and disadvantages of SC-GLDPC codes are discussed.