Two Classes of Broadcast Channels With Side-Information: Capacity Outer Bounds

Abstract: In this paper, we derive outer bounds on the capacity region of two classes of the general two-user discrete memoryless broadcast channels with side-information at the transmitter. The first class comprises the classical broadcast channel where a sender transmits two independent messages to two receivers. A constraint that each message must be kept confidential from the unintended receiver constitutes the second class. For both classes, the conditional distribution characterizing the channel depends on a state process and the encoder has side-information provided to it in a noncausal manner. For the first class of channels, an outer bound is derived employing techniques used to prove the converse theorem for the Gel'fand-Pinsker's channel with random parameters; the bounds are tight for individual rate constraints, but can be improved upon for the sum rate. The technique for deriving outer bounds for the second class of channels hinges on the confidentiality requirements; we also derive a genie-aided outer bound, where a hypothetical genie gives the unintended message to a receiver which treats it as side-information during equivocation computation. For both classes of channels, Csisz\'{a}r's sum identity plays a central role in establishing the capacity outer bounds.