Three-Receiver Broadcast Channel with Side Information

TL;DR

This paper derives achievable rate regions for three-receiver broadcast channels with side information, extending known results and establishing tight bounds for various classes, including deterministic and semi-deterministic channels.

Contribution

It introduces new achievable rate regions for 3-receiver BC with side information, generalizes existing results, and proves capacity invariance in certain deterministic cases.

Findings

Rate regions for multilevel BC with side information are derived.

Achievable regions are tight for several classes of 3-receiver BC.

Side information does not affect capacity for deterministic receivers.

Abstract

Three-Receiver broadcast channels (BC) are of interest due to their information-theoretic differences with two-receiver one. In this paper, we derive achievable rate regions for two classes of 3-receiver BC with side information (SI), i.e. Multilevel BC (MBC) and 3-receiver less noisy BC, using a combination of superposition coding, Gelfand-Pinsker binning scheme and Nair-El Gamal indirect decoding. Our rate region for MBC subsumes Steinberg rate region for 2-receiver degraded BC with SI as its special case. We will also show that the obtained achievable rate regions in the first two cases are tight for several classes of non-deterministic, semi-deterministic, and deterministic 3-receiver BC when SI is available both at the transmitter and at the receivers. We also prove that as far as a receiver is deterministic in the three-receiver less noisy BC, the presence of side information at that receiver does not affect the capacity region. We have also provided the writing on dirty paper (WDP) property for 3-receiver BC is provided as an example. In the last section, we provide simple bounds on the capacity region of the Additive Exponential noise three-receiver broadcast channels with Additive Exponential interference (AEN-3BC-EI).