An information inequality and evaluation of Marton´s inner bound for binary input broadcast channels

We establish an information inequality that is intimately connected to the evaluation of the sum rate given by Marton´s inner bound for two-receiver broadcast channels with a binary input alphabet. This generalizes a recent result where the inequality was established for a particular channel, the binary skew-symmetric broadcast channel. The inequality implies that randomized time-division strategy indeed achieves the sum rate of Marton´s inner bound for all binary input broadcast channels.