High-Rate Spatially Coupled LDPC Codes Based on Massey's Convolutional Self-Orthogonal Codes

TL;DR

This paper introduces a new class of high-rate spatially coupled LDPC codes based on Massey's convolutional self-orthogonal codes, demonstrating their strong performance and decoding efficiency through theoretical analysis and numerical results.

Contribution

The paper presents a novel construction of high-rate SC-LDPC codes using convolutional self-orthogonal codes, including a non-systematic variant with guaranteed girth and free distance.

Findings

Achieve excellent performance at very high rates

Comparable decoding thresholds to existing SC-LDPC codes

Maintain girth and free distance properties after lifting

Abstract

In this paper, we study a new class of high-rate spatially coupled LDPC (SC-LDPC) codes based on the convolutional self-orthogonal codes (CSOCs) first introduced by Massey. The SC-LDPC codes are constructed by treating the irregular graph corresponding to the parity-check matrix of a systematic rate R = (n - 1)/n CSOC as a convolutional protograph. The protograph can then be lifted using permutation matrices to generate a high-rate SC-LDPC code whose strength depends on the lifting factor. The SC-LDPC codes constructed in this fashion can be decoded using iterative belief propagation (BP) based sliding window decoding (SWD). A non-systematic version of a CSOC parity-check matrix is then proposed by making a slight modification to the systematic construction. The non-systematic parity-check matrix corresponds to a regular protograph whose degree profile depends on the rate and error-correcting capability of the underlying CSOC. Even though the parity-check matrix is in non-systematic form, we show how systematic encoding can still be performed. We also show that the non-systematic convolutional protograph has a guaranteed girth and free distance and that these properties carry over to the lifted versions. Finally, numerical results are included demonstrating that CSOC-based SC-LDPC codes (i) achieve excellent performance at very high rates, (ii) have performance at least as good as that of SC-LDPC codes constructed from convolutional protographs commonly found in the literature, and (iii) have iterative decoding thresholds comparable to those of existing SC-LDPC code designs.