On the Evaluation of Marton’s Inner Bound for Two-Receiver Broadcast Channels

Marton’s inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized-time-division strategy achieves every rate triple in Marton’s region for binary input broadcast channels. This extends the result by Hajek and Pursley which showed that the Cover-van der Muelen region was exhausted by the randomized-time-division strategy.