REDUCED-REDUNDANCY PRODUCT CODES FOR BURST ERROR-CORRECTION

In a typical burst error correction application of a product code of n (v) x n(h) arrays, one uses an [n(h), n(h) - r(h)] code C-h that detec ts corrupted rows, and an [n(v), n(v) - r(v)] code C-v that is applied to the columns while regarding the detected corrupted rows as erasure s, Although this conventional product code scheme offers very good err or protection, it contains excessive redundancy, due to the fact that the code C-h provides the code C-v with information on many error patt erns that exceed the correction capability of C-v. In this work, a cod ing scheme is proposed in which this excess redundancy is eliminated, resulting in significant savings in the overall redundancy compared to the conventional case, while offering the same error protection. The redundancy of the proposed scheme is n(h)r(v) + r(h)(ln r(v) + O(1)) r(v), where the parameters r(h) and r(v) are close in value to their counterparts in the conventional case, which has redundancy n(h)r(v) n(v)r(h) - r(h)r(v). In particular, when the codes C-h and C-v have t he same rate and r(h) much less than n(h), the redundancy of the propo sed scheme is close to one-half of that of the conventional product co de counterpart. Variants of the scheme are presented for channels that are mostly bursty, and for channels with a combination of random erro rs and burst errors.