On Symbol Versus Bit Interleaving for Block-Coded Binary Markov Channels

We examine bit- and symbol-interleaving strategies for linear nonbinary block codes (under bounded-distance decoding) over the family of binary additive noise finite-state Markov channel (FSMC) models with memory. We derive a simple analytical sufficient condition under which perfect (i.e., with infinite interleaving depth) symbol interleaving outperforms perfect bit interleaving in terms of the probability of codeword error (PCE). It is shown that the well-known Gilbert–Elliott channel (GEC) with positive noise-correlation coefficient and the recently introduced Markovian queue-based channel (QBC) of memory $M$ satisfy this condition. This result has widely been illustrated numerically (without proof) in the literature, particularly for the GEC. We also provide examples of binary FSMC models for which the reverse result holds, i.e., perfect bit interleaving outperforming perfect symbol interleaving. Finally, a numerical PCE study of imperfect symbol-interleaved nonbinary codes over the QBC indicates that there is a linear relationship between the optimal interleaving depth and a function of a single parameter of the QBC.