Expurgated Bounds for the Asymmetric Broadcast Channel

This paper contains two main contributions concerning the expurgation of hierarchical ensembles for the asymmetric broadcast channel. The first is an analysis of the optimal maximum likelihood (ML) decoders for the weak and strong user. Two different methods of code expurgation will be used, that will provide two competing error exponents. The second is the derivation of expurgated exponents under the generalized stochastic likelihood decoder (GLD). We prove that the expurgated exponents achieved for the hierarchical ensemble under GLD decoding are at least as good as the maximum between the random coding error exponents derived in an earlier work by Averbuch and Merhav (2018) and one of our ML-based expurgated exponents.