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.