On optimal low-complexity source/channel coding

Shannon's separation theorem gives a conceptually and practically appealing way to construct an optimal communication system in two independent steps, namely source compression and channel coding. However, sometimes it is worth considering {\em joint} source/ channel coding instead. In fact, for certain source/channel pairs, not using any code at all already achieves the optimum performance. For a larger class ${\mathbb S}$ of source/channel pairs, there exists a single-letter code with optimal performance. In this paper, we consider the class of {\em discrete memoryless} source/channel pairs for which a code of finite block length $M$ achieves optimal performance. Somewhat contrary to (initial) intuition, it seems that this class is not larger than ${\mathbb S}$.