Performance of Interleaved Non-Binary Block Codes Over Binary Channels with Memory

The performance of Reed-Solomon codes over two classes of binary channels with memory, the queue-based channel (QBC) and the Gilbert-Elliott channel (GEC) is analyzed under the assumption of bounded distance decoding. In particular, we examine two interleaving strategies encountered when dealing with non-binary codes over a binary channel; namely, symbol interleaving and bit interleaving. An analytical proof is given demonstrating that perfect (i.e., with infinite interleaving depth) symbol interleaving results in a better performance compared to perfect bit interleaving for any non-binary block code over either the QBC or the GEC with positive noise correlation coefficient. Next, the effect of imperfect interleaving on the code performance is examined. An enumerative approach is applied to derive some useful analytical expressions pertaining to the calculation of the probability of codeword error (PCE) for the simplest scenario of the QBC which is the additive first-order Markov noise channel. Numerical results for PCE are provided for more general QBC models and the GEC. The performance of imperfect interleaved binary codes with imperfect interleaved non-binary codes is compared and the choice of the interleaving depth to achieve a required performance is discussed for different values of the channel parameters.