Open AccessModule minimisation based low‐complexity soft decoding of Reed–Solomon codes
Author(s) -
Xing Jiongyue,
Chen Li,
Bossert Martin
Publication year - 2019
Publication title -
iet communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.355
H-Index - 62
eISSN - 1751-8636
pISSN - 1751-8628
DOI - 10.1049/iet-com.2019.0064
Subject(s) - decoding methods , list decoding , computer science , berlekamp–welch algorithm , algorithm , interpolation (computer graphics) , reed–solomon error correction , sequential decoding , computational complexity theory , hamming code , benchmark (surveying) , mathematics , linear code , concatenated error correction code , artificial intelligence , block code , motion (physics) , geodesy , geography
The interpolation‐based algebraic decoding for Reed–Solomon (RS) codes can correct errors beyond half of the code's minimum Hamming distance. Using soft information, the algebraic soft decoding (ASD) further improves the decoding performance. This paper presents a unified study of two classical ASD algorithms, the algebraic Chase decoding and the Koetter‐Vardy decoding. Their computationally expensive interpolation is solved by the module minimisation (MM) technique which consists of basis construction and basis reduction. Compared with Koetter's interpolation, the MM interpolation yields a smaller computational cost for the two ASD algorithms. Re‐encoding transform is further applied to reduce the decoding complexity by reducing the degree of module generators. Based on assessing the degree of module seeds, a complexity reducing approach is introduced to further facilitate the two ASD algorithms. Computational cost of the two algorithms as well as their re‐encoding transformed variants will be analysed. Performance of the two ASD algorithms will be compared under decoding expenditure benchmark, providing more practical insights of their applications.