Exact Random Coding Exponents and Universal Decoders for the Asymmetric Broadcast Channel

摘要

This work contains two main contributions concerning the asymmetric broadcastchannel. The first is an analysis of the exact random coding error exponentsfor both users, and the second is the derivation of universal decoders for bothusers. These universal decoders are certain variants of the maximum mutualinformation (MMI) universal decoder, which achieve the corresponding randomcoding exponents of optimal decoding. In addition, we introduce some lowerbounds, which involve optimization over very few parameters, unlike theoriginal, exact exponents, which involve minimizations over auxiliaryprobability distributions. Numerical results for the binary symmetric broadcastchannel show improvements over previously derived error exponents for the samemodel.