Achievability bounds for unequal message protection at finite block lengths

We study achievability bounds for a class of unequal error protection codebooks with m > 1 different classes of codewords called unequal message protection (UMP) codes. We extend the dependence testing bound due to Polyanskiy-Poor-Verdú to be applicable to UMP codes and use this extension to obtain refined asymptotic expansions for the performance of such codes over discrete memoryless channels. In addition, we consider two questions related to the practical construction of UMP codes. First, we study a “header” construction that prefixes the message class into a header followed by data protection using a standard homogeneous (classical) code. We show that, in general, this construction is not optimal at finite block lengths. We further demonstrate that our main UMP achievability bound can be obtained using coset codes, which suggests a path to tractable implementation of UMP codes.