An Information Inequality and Evaluation of Marton's Inner Bound for Binary Input Broadcast Channels

We establish an information inequality concerning five random variables. This inequality is motivated by the sum-rate evaluation of Marton's inner bound for two receiver broadcast channels with a binary input alphabet. We establish that randomized time-division strategy achieves the sum rate of Marton's inner bound for all binary input broadcast channels. We also obtain an improved cardinality bound for evaluating the maximum sum rate given by Marton's inner bound for all broadcast channels. Using these tools we explicitly evaluate the inner and outer bounds for the binary skew-symmetric broadcast channel and demonstrate a gap between the bounds.