An information inequality for the BSSC broadcast channel

We establish an information theoretic inequality concerning the binary skew-symmetric broadcast channel that was conjectured by one of the authors. This inequality helps to quantify the gap between the sum rate obtained by Marton´s inner bound and the Nair-El Gamal´s outer bound for the binary skew-symmetric broadcast channel. We also establish that it suffices to consider |W| ¿ |X| for evaluating the maximum sum rate in Marton´s inner bound for arbitrary broadcast channels. The main technique used is an extension and modification of the ideas present in a recent paper by Gohari and Anantharam.