Open AccessBCH CODES DECODER BASED ON EUCLID ALGORITHM
Author(s) -
Boris Filippov
Publication year - 2021
Publication title -
synchroinfo journal
Language(s) - English
Resource type - Journals
eISSN - 2664-0678
pISSN - 2664-066X
DOI - 10.36724/2664-066x-2021-7-2-14-17
Subject(s) - bch code , berlekamp–welch algorithm , algorithm , galois theory , polynomial , decoding methods , mathematics , computer science , soft decision decoder , reed–solomon error correction , sequential decoding , discrete mathematics , linear code , block code , mathematical analysis
In the process of algebraic decoding of BCH codes over the field GF(q) with the word length n = qm-1, correcting t errors, both in the time and frequency domains, it is necessary to find the error locator polynomial ?(x) as the least polynomial for which the key equation. Berlekamp proposed a simple iterative scheme, which was called the Berlekamp-Messi algorithm, and is currently used in most practical applications. Comparative statistical tests of the proposed decoder and decoder using the Berlikamp-Messi algorithm showed that they differ slightly in decoding speed. The proposed algorithm is implemented in the environment in Turbo Pascal and can be used for the entire family of BCH codes by replacing the primitive Galois polynomial.