On the Minimum/Stopping Distance of Array Low-Density Parity-Check Codes

In this work, we study the minimum/stopping distance of array low-density parity-check (LDPC) codes. An array LDPC code is a quasi-cyclic LDPC code specified by two integers q and m, where q is an odd prime and m <= q. In the literature, the minimum/stopping distance of these codes (denoted by d(q,m) and h(q,m), respectively) has been thoroughly studied for m <= 5. Both exact results, for small values of q and m, and general (i.e., independent of q) bounds have been established. For m=6, the best known minimum distance upper bound, derived by Mittelholzer (IEEE Int. Symp. Inf. Theory, Jun./Jul. 2002), is d(q,6) <= 32. In this work, we derive an improved upper bound of d(q,6) <= 20 and a new upper bound d(q,7) <= 24 by using the concept of a template support matrix of a codeword/stopping set. The bounds are tight with high probability in the sense that we have not been able to find codewords of strictly lower weight for several values of q using a minimum distance probabilistic algorithm. Finally, we provide new specific minimum/stopping distance results for m <= 7 and low-to-moderate values of q <= 79.Comment: To appear in IEEE Trans. Inf. Theory. The material in this paper was presented in part at the 2014 IEEE International Symposium on Information Theory, Honolulu, HI, June/July 201

Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications

Coding; Communications; Engineering; Networks; Information Theory; Algorithm

A II-HARQ scheme for BEC models with ML decoding of Turbo Codes

In this paper we propose a coding-decoding scheme to be used for II-type hybrid ARQ on a binary erasure channel model, based on rate compatible punctured binary Turbo Codes, DRP interleaver design and ML decoding at the receiver. We carefully design the interleaver and the puncturing mask, and we describe how to achieve low-complexity Maximum Likelihood decoding. We show for the case of an MPEG2 packet size that this scheme overrides random codes upper bounds, providing throughputs within 0.05 bits from capacity at word error rates greater or equal to 1e-6