Achievable Rate Region for Three User Discrete Broadcast Channel Based on Coset Codes
Arun Padakandla, S. Sandeep Pradhan · IEEE Transactions on Information Theory · 2018
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 1 M-region. We propose a coding technique based on coset codes that yield an achievable rate triple not contained within 1 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.