Results on Parity-Check Matrices With Optimal Stopping And/Or Dead-End Set Enumerators

The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the parity-check matrix representing the code. In this correspondence, we introduce the notion of dead-end sets to explicitly demonstrate this dependency. The choice of the parity-check matrix entails a tradeoff between performance and complexity. We give bounds on the complexity of iterative decoders achieving optimal performance in terms of the sizes of the underlying parity-check matrices. Further, we fully characterize codes for which the optimal stopping set enumerator equals the weight enumerator.TelecommunicationsElectrical Engineering, Mathematics and Computer Scienc

On the existence of optimum cyclic burst-correcting codes

It is shown that for each integerb geq 1infinitely many optimum cyclicb-burst-correcting codes exist, i.e., codes whose lengthn, redundancyr, and burst-correcting capabilityb, satisfyn = 2^{r-b+1} - 1. Some optimum codes forb = 3, 4, and5are also studied in detail