Capacity Bounds for State-Dependent Broadcast Channels

TL;DR

This paper establishes theoretical capacity bounds for three classes of two-user state-dependent broadcast channels with noncausal side-information, addressing rate penalties and confidentiality constraints in complex communication scenarios.

Contribution

It introduces new inner and outer bounds for these channels, including explicit sum-rate bounds and gap analysis, advancing understanding of capacity limits under various constraints.

Findings

Derived inner bounds for all three channel classes.

Characterized rate penalties due to side-information and confidentiality.

Outer bounds within a fixed gap for certain channel classes.

Abstract

In this paper, we derive information-theoretic performance limits for three classes of two-user state-dependent 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. We derive inner bounds for all the three classes of channels. For the first and second class of channels, we discuss the rate penalty on the achievable region for having to deal with side-information. For channels of third class, we characterize the rate penalties for having to deal not only with side-information, but also to satisfy confidentiality constraints. We then derive outer bounds, where we present an explicit characterization of sum-rate bounds for the first and third class of channels. For channels of the second class, we show that our outer bounds are within a fixed gap away from the achievable rate region, where the gap is independent of the distribution characterizing this class of channels. The channel models presented in this paper are useful variants of the classical broadcast channel, and provide fundamental building blocks for cellular downlink communications with side-information, such as fading in the wireless medium, interference caused by neighboring nodes in the network, {\etc}. at the encoder; two-way relay communications; and secure wireless broadcasting.