Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance
This work addresses decoding challenges in coding theory for applications like data storage and communications, presenting incremental improvements with new bounds and algorithms.
The authors tackled the problem of decoding repeated-root cyclic codes by generalizing known bounds on minimum distance and introducing two burst error decoding algorithms, achieving guaranteed decoding radii and quadratic-time probabilistic decoding.
The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root cyclic codes and present a syndrome-based burst error decoding algorithm with guaranteed decoding radius based on an associated folded cyclic code. Furthermore, we present a third technique for bounding the minimum Hamming distance based on the embedding of a given repeated-root cyclic code into a repeated-root cyclic product code. A second quadratic-time probabilistic burst error decoding procedure based on the third bound is outlined. Index Terms Bound on the minimum distance, burst error, efficient decoding, folded code, repeated-root cyclic code, repeated-root cyclic product code