On State-Dependent Broadcast Channels, with Side-Information at the Transmitter

In this paper, we derive information-theoretic performance limits for three classes of two-user statedependent discrete memoryless broadcast channels, with noncausal side-information at the encoder. The first class of channels comprises a sender broadcasting two independent messages to two non-cooperating receivers; for channels of the second class, each receiver is given the message it need not decode; and the third class comprises channels where the sender is constrained to keep each message confidential from the unintended receiver. To derive inner bounds, we employ an extension of Marton’s achievability scheme for the classical two-user broadcast channel, results from the second moment method, an extension of the technique proposed by Kramer and Shamai for broadcast channels with receiver side-information, and stochastic encoders to satisfy confidentiality requirements. Outer bounds are derived by following the procedure used to prove the converse theorem for Gel’fand-Pinsker’s channels with random parameters; and confidentiality constraints are utilized for deriving outer bounds for channels belonging to the third class. For channels of the second class, the bounds are tight, thereby yielding the capacity region. Index Terms State-dependent broadcast channels, side-information, rate regions, outer bounds. The authors would like to thank Parthajit Mohapatra for helpful comments and discussion. The authors would also like to thank Tobias Oechtering, for pointing out an error in an earlier draft of this paper, in the proof of Theorem 3.2. ar X iv :1 11 0. 01 24 v5 [ cs .I T ] 2 2 N ov 2 01 1