On algebraic soft-decision decoding algorithms for BCH codes
In this paper, three algebraic soft-decision decoding algorithms are presented for binary Bose-Chaudhuri-Hocquengham (BCH) codes. Two of these algorithms are based on the bounded distance (BD) +1 generalized minimum-distance (GMD) decoding presented by Berlekamp, and the other is based on Chase decoding. A simple algebraic algorithm is first introduced, and it forms a common basis for the decoding algorithms presented here. Next, efficient ED +1 GMD and ED +2 GMD decoding algorithms are presented. It is shown that, for binary BCH codes with odd designed-minimum-distance d and length n, both the ED +1 GMD and the ED +2 GMD decoding algorithms can be performed with complexity O(nd), The error performance of these decoding algorithms is shown to be significantly superior to that of conventional GMD decoding by computer simulation. Finally, an efficient algorithm is presented for Chase decoding of binary BCH codes. Like a one-pass GMD decoding algorithm, this algorithm produces all necessary error-locator polynomials for Chase decoding in one run.
generalized minimum-distance (gmd) decoding chase decoding bose-chaudhuri-hocquenghem (bch) codes bounded distance plus t gmd decoding decoding complexity soft decision decoding