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We establish an information inequality that is intimately connected to theevaluation of the sum rate given by Marton's inner bound for two receiverbroadcast channels with a binary input alphabet. This generalizes a recentresult where the inequality was established for a particular channel, thebinary skew-symmetric broadcast channel. The inequality implies that randomizedtime-division strategy indeed achieves the sum rate of Marton's inner bound forall binary input broadcast channels.

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