On computing the performance of linear block codes in nonindependent channel errors

We present an analytical method to compute the exact performance of algebraically decoded linear block codes in nonindependent channel errors. Performance is computed by rating decoding events. The block error distribution and the coset probabilities are of fundamental interest. A recursion in matrix notation is taken to compute the block error distribution. By using an automata model of the channel-decoder-cascade, coset probabilities can be computed directly in an original domain. Alternatively, the analysis can be performed in a spectral domain having a simpler structure. The relationship between both domains is given by a Walsh-Hadamard transform. Aspects of implementation are discussed and examples are presented to illustrate the efficiency of the method