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

Costello, Daniel J. ; Zhu, Min ; Mitchell, David G.M. and Lentmaier, Michael LU (2025) 2025 IEEE International Symposium on Information Theory, ISIT 2025
Abstract

We propose a new class of high-rate spatially coupled LDPC (SC-LDPC) codes based on the convolutional selforthogonal codes (CSOCs) first introduced by Massey. The SCLDPC 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 based sliding window decoding. To improve performance, a non-systematic version of a C SOC parity-check matrix is then proposed by making a slight modification to the... (More)

We propose a new class of high-rate spatially coupled LDPC (SC-LDPC) codes based on the convolutional selforthogonal codes (CSOCs) first introduced by Massey. The SCLDPC 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 based sliding window decoding. To improve performance, a non-systematic version of a C SOC parity-check matrix is then proposed by making a slight modification to the systematic construction. 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. Numerical results are included demonstrating that CSOC-based SC-LDPC codes (i) have performance at least as good as that of SC-LDPC codes commonly found in the literature, and (ii) have iterative decoding thresholds comparable to those of existing SC-LDPC code designs.

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author
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organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2025 IEEE International Symposium on Information Theory : Proceedings - Proceedings
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
2025 IEEE International Symposium on Information Theory, ISIT 2025
conference location
Ann Arbor, United States
conference dates
2025-06-22 - 2025-06-27
external identifiers
  • scopus:105021936019
ISBN
9798331543990
DOI
10.1109/ISIT63088.2025.11195322
language
English
LU publication?
yes
id
57b84f11-9aaf-4e39-9cd2-1e20080d0a2f
date added to LUP
2026-02-10 14:01:03
date last changed
2026-02-10 14:02:10
@inproceedings{57b84f11-9aaf-4e39-9cd2-1e20080d0a2f,
  abstract     = {{<p>We propose a new class of high-rate spatially coupled LDPC (SC-LDPC) codes based on the convolutional selforthogonal codes (CSOCs) first introduced by Massey. The SCLDPC 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 based sliding window decoding. To improve performance, a non-systematic version of a C SOC parity-check matrix is then proposed by making a slight modification to the systematic construction. 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. Numerical results are included demonstrating that CSOC-based SC-LDPC codes (i) have performance at least as good as that of SC-LDPC codes commonly found in the literature, and (ii) have iterative decoding thresholds comparable to those of existing SC-LDPC code designs.</p>}},
  author       = {{Costello, Daniel J. and Zhu, Min and Mitchell, David G.M. and Lentmaier, Michael}},
  booktitle    = {{2025 IEEE International Symposium on Information Theory : Proceedings}},
  isbn         = {{9798331543990}},
  language     = {{eng}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{High-Rate Spatially Coupled LDPC Codes Based on Massey's Convolutional Self-Orthogonal Codes}},
  url          = {{http://dx.doi.org/10.1109/ISIT63088.2025.11195322}},
  doi          = {{10.1109/ISIT63088.2025.11195322}},
  year         = {{2025}},
}