An efficient combination between Berlekamp-Massey and Hartmann Rudolph algorithms to decode BCH codes

Hamza Faham, My Seddiq El Kasmi Alaoui, Saïd Nouh, Mohamed Azzouazi

Abstract


In digital communication and storage systems, the exchange of data is achieved using a communication channel which is not completely reliable. Therefore, detection and correction of possible errors are required by adding redundant bits to information data. Several algebraic and heuristic decoders were designed to detect and correct errors. The Hartmann Rudolph (HR) algorithm enables to decode a sequence symbol by symbol. The HR algorithm has a high complexity, that's why we suggest using it partially with the algebraic hard decision decoder Berlekamp-Massey (BM).
In this work, we propose a concatenation of Partial Hartmann Rudolph (PHR) algorithm and Berlekamp-Massey decoder to decode BCH (Bose-Chaudhuri-Hocquenghem) codes. Very satisfying results are obtained. For example, we have used only 0.54% of the dual space size for the BCH code (63,39,9) while maintaining very good decoding quality. To judge our results, we compare them with other decoders.

Keywords


Error correcting codes; Hartmann Rudolph; Berlekamp Massey; PHR-BM; BCH codes

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DOI: http://dx.doi.org/10.21533/pen.v6i2.540

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Copyright (c) 2019 Hamza FAHAM, My Seddiq EL KASMI ALAOUI, Saïd NOUH, Mohamed AZZOUAZI

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN: 2303-4521

Digital Object Identifier DOI: 10.21533/pen

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License