Performance of multiple-step (T,U) permutation decoding of cyclic codes

The performance of multiple-step (T,U) permutation decoding of cyclic codes is presented. First, the error-free gaps in a permuted error pattern are studied. It is shown that the gap-lengths in any two permuted error patterns are related by a linear mapping. Based on the characteristics of error-free gaps, the capability of multiple-step (T,U) permutation decoding of (n,k,2t+1) cyclic codes with odd t is examined. The bounds on the code rate of permutation-decodable binary cyclic codes are subsequently derived. It is shown that the code rate can be increased by increasing the number of U-permutations. For a permutation-decodable (n,k,2t+1) cyclic code, there is an optimum permutation step which makes the largest increase in its code rate. Examples are also given to illustrate the applications of the analytical results