Chen Chen;Fengfan Yang;Hongjun Xu;Lawrence Muthama Paul
{"title":"Optimized design of quasi-GRS codes with multi-step simplified MLD","authors":"Chen Chen;Fengfan Yang;Hongjun Xu;Lawrence Muthama Paul","doi":"10.23919/JCN.2025.000004","DOIUrl":null,"url":null,"abstract":"In this manuscript, inspired by the special construction of generalized Reed-Solomon (GRS) codes, we prove that any linear block code can be contained by a high-dimensional GRS code from the perspective of the isomorphism between the code space and the polynomial space. Then, a new code family, named quasi-GRS codes, is constructed, which can exactly contain a GRS code of lower 1-dimensional (1-D) and be contained by a higher 1-D GRS code. Furthermore, the exhaustive search approach is developed to assist in selecting the quasi-GRS code with the optimal code weight distribution. In addition, a multi-step simplified maximum likelihood decoding (MSS-MLD) is proposed to efficiently decode the quasi-GRS coding scheme, whose decoding complexity is significantly reduced at an acceptable performance loss compared to the optimal MLD. From the Monte-Carlo simulation, the optimized quasi-GRS coding scheme outperforms the existing non-binary Bose-Chaudhuri-Hocquenghem (BCH) coding scheme with a similar code rate by a margin of over 1 dB at the high signal-to-noise (SNR) region under identical channel conditions.","PeriodicalId":54864,"journal":{"name":"Journal of Communications and Networks","volume":"27 1","pages":"40-49"},"PeriodicalIF":2.9000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10923676","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Communications and Networks","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10923676/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this manuscript, inspired by the special construction of generalized Reed-Solomon (GRS) codes, we prove that any linear block code can be contained by a high-dimensional GRS code from the perspective of the isomorphism between the code space and the polynomial space. Then, a new code family, named quasi-GRS codes, is constructed, which can exactly contain a GRS code of lower 1-dimensional (1-D) and be contained by a higher 1-D GRS code. Furthermore, the exhaustive search approach is developed to assist in selecting the quasi-GRS code with the optimal code weight distribution. In addition, a multi-step simplified maximum likelihood decoding (MSS-MLD) is proposed to efficiently decode the quasi-GRS coding scheme, whose decoding complexity is significantly reduced at an acceptable performance loss compared to the optimal MLD. From the Monte-Carlo simulation, the optimized quasi-GRS coding scheme outperforms the existing non-binary Bose-Chaudhuri-Hocquenghem (BCH) coding scheme with a similar code rate by a margin of over 1 dB at the high signal-to-noise (SNR) region under identical channel conditions.
期刊介绍:
The JOURNAL OF COMMUNICATIONS AND NETWORKS is published six times per year, and is committed to publishing high-quality papers that advance the state-of-the-art and practical applications of communications and information networks. Theoretical research contributions presenting new techniques, concepts, or analyses, applied contributions reporting on experiences and experiments, and tutorial expositions of permanent reference value are welcome. The subjects covered by this journal include all topics in communication theory and techniques, communication systems, and information networks. COMMUNICATION THEORY AND SYSTEMS WIRELESS COMMUNICATIONS NETWORKS AND SERVICES.