Performance of concatenated Reed-Solomon and turbo codes with non ideal interleaving

The performance of a Reed-Solomon (RS) code has an analytical expression if the errors at the input of the decoder are independent. In concatenated schemes, this condition is often obtained through an interleaving device disrupting the correlation between erroneous symbols. Sometimes the ideal depth of such interleaver is too large to implement, and the RS decoder must operate in suboptimal conditions, for which no analytical formulas are available. In this paper, we present a statistical model that allows analytical evaluation of the performances of a concatenated scheme with an inner turbo code and an outer RS code, in the case of under-dimensioned interleavers. The model requires a statistical analysis of the erroneous symbols at the output of the inner decoder.