Achievable Rate Region for Three User Discrete Broadcast Channel Based on Coset Codes

Abstract

We consider the problem of developing coding techniques and deriving achievable rate regions for discrete memoryless broadcast channels with three receivers (3-DBC). We begin by identifying a novel vector additive 3-DBC for which we characterize an upper bound on the the largest achievable rate region based on unstructured codes, henceforth referred to as $\pmb {\mathscr {U}}\mathcal {M}$ -region. We propose a coding technique based on coset codes that yield an achievable rate triple not contained within $\pmb {\mathscr {U}}\mathcal {M}$ -region. We generalize the proposed coding technique using a new ensemble of codes— partitioned coset codes (PCC)—containing both empirical and algebraic properties, and evaluate its performance to derive an achievable rate region for the general 3-DBC. The new elements in this derivation are binning and joint typicality encoding and decoding of statistically correlated PCCs. We validate the utility of this technique by identifying non-additive instances of 3-DBC for which the proposed coding techniques based on PCC yield strictly larger rates.