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Error Exponents of LDPC Codes under Low-Complexity Decoding
This paper deals with the specific construction of binary low-density parity-check (LDPC) codes. We derive lower bounds on the error exponents for these codes transmitted over the memoryless binary symmetric channel (BSC) for both the well-known maximum-likelihood (ML) and proposed low-complexity de...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7926880/ https://www.ncbi.nlm.nih.gov/pubmed/33671792 http://dx.doi.org/10.3390/e23020253 |
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author | Rybin, Pavel Andreev, Kirill Zyablov, Victor |
author_facet | Rybin, Pavel Andreev, Kirill Zyablov, Victor |
author_sort | Rybin, Pavel |
collection | PubMed |
description | This paper deals with the specific construction of binary low-density parity-check (LDPC) codes. We derive lower bounds on the error exponents for these codes transmitted over the memoryless binary symmetric channel (BSC) for both the well-known maximum-likelihood (ML) and proposed low-complexity decoding algorithms. We prove the existence of such LDPC codes that the probability of erroneous decoding decreases exponentially with the growth of the code length while keeping coding rates below the corresponding channel capacity. We also show that an obtained error exponent lower bound under ML decoding almost coincide with the error exponents of good linear codes. |
format | Online Article Text |
id | pubmed-7926880 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-79268802021-03-04 Error Exponents of LDPC Codes under Low-Complexity Decoding Rybin, Pavel Andreev, Kirill Zyablov, Victor Entropy (Basel) Article This paper deals with the specific construction of binary low-density parity-check (LDPC) codes. We derive lower bounds on the error exponents for these codes transmitted over the memoryless binary symmetric channel (BSC) for both the well-known maximum-likelihood (ML) and proposed low-complexity decoding algorithms. We prove the existence of such LDPC codes that the probability of erroneous decoding decreases exponentially with the growth of the code length while keeping coding rates below the corresponding channel capacity. We also show that an obtained error exponent lower bound under ML decoding almost coincide with the error exponents of good linear codes. MDPI 2021-02-22 /pmc/articles/PMC7926880/ /pubmed/33671792 http://dx.doi.org/10.3390/e23020253 Text en © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Rybin, Pavel Andreev, Kirill Zyablov, Victor Error Exponents of LDPC Codes under Low-Complexity Decoding |
title | Error Exponents of LDPC Codes under Low-Complexity Decoding |
title_full | Error Exponents of LDPC Codes under Low-Complexity Decoding |
title_fullStr | Error Exponents of LDPC Codes under Low-Complexity Decoding |
title_full_unstemmed | Error Exponents of LDPC Codes under Low-Complexity Decoding |
title_short | Error Exponents of LDPC Codes under Low-Complexity Decoding |
title_sort | error exponents of ldpc codes under low-complexity decoding |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7926880/ https://www.ncbi.nlm.nih.gov/pubmed/33671792 http://dx.doi.org/10.3390/e23020253 |
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