Performance of Reed-Solomon codes in concatenated schemes with non ideal interleaving

The prediction of the performance of a Reed–Solomon (RS) code has an analytical solution in case of statistical independence of the errors at the input of the RS decoder (RSD). 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 RSD must operate in sub-optimal conditions, for which no analytical formulas are available. In this paper, we propose a statistical model that can manage under-dimensioned interleavers. With a mild set of hypotheses on the behaviour of the inner decoder (ID), we derive analytical expressions for the performance of the concatenated code. Input data for the model can be analytical or can be obtained by simulation. We apply the method to two different types of inner codes, namely turbo codes and RS codes, and we compare the results predicted by the model with those obtained through simulation, when available, showing a very good agreement.