Reduced-Redundancy Product Codes for Burst Error Correction

In a typical burst-error correction application of a product code of nv nh arrays, one uses an [nh; nh rh] code Ch that detects corrupted rows, and an [nv; nv rv] code Cv that is applied to the columns while regarding the detected corrupted rows as erasures. Although this conventional product code scheme o ers very good error protection, it contains excessive redundancy, due to the fact that the code Ch provides the code Cv with information on many error patterns that exceed the correction capability of Cv. In this work, a coding scheme is proposed in which this excess redundancy is eliminated, resulting in signi cant savings in the overall redundancy compared to the conventional case, while o ering the same error protection. The redundancy of the proposed scheme is nhrv+rh(ln rv+O(1))+rv, where the parameters rh and rv are close in value to their counterparts in the conventional case, which has redundancy nhrv + nvrh rhrv. In particular, when the codes Ch and Cv have the same rate and rh nh, the redundancy of the proposed scheme is close to one half of that of the conventional product code counterpart. Variants of the scheme are presented for channels that are mostly bursty, and for channels with a combination of random errors and burst errors.