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

2025-02-06

AI Summary

This work addresses the challenges of constructing high-rate spatially coupled LDPC (SC-LDPC) codes and their performance limitations. We introduce, for the first time, Massey’s convolutional self-orthogonal codes (CSOC) into SC-LDPC design. A non-systematic CSOC-based protograph construction method is proposed; combined with protograph lifting and carefully designed permutation matrices, it yields high-rate SC-LDPC codes while guaranteeing both girth and free distance after lifting. Efficient systematic encoding is further achieved under the non-systematic protograph. The resulting codes support sliding-window belief propagation decoding. At extremely high code rates (e.g., ≥ 0.95), they achieve significantly superior bit-error-rate performance compared to state-of-the-art constructions, with decoding thresholds matching those of mainstream SC-LDPC designs—and exceeding those of typical convolutional protograph-based schemes. The core innovations are the novel integration of CSOC with SC-LDPC and a non-systematic-protograph-driven paradigm for high-performance, high-rate code construction.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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.

Problem

• Develop high-rate SC-LDPC codes
• Utilize Massey's convolutional self-orthogonal codes
• Enhance error-correcting with iterative decoding

Innovation

• High-rate SC-LDPC codes
• Convolutional self-orthogonal codes
• Iterative belief propagation decoding