Capacity Theorems for Broadcast Channels with Two Channel State Components Known at the Receivers

TL;DR

This paper determines the capacity regions of certain broadcast channels with two possible channel states known only at the receivers, using Marton coding for deterministic cases and Gaussian inputs for degraded Gaussian channels.

Contribution

It introduces new capacity theorems for broadcast channels with two channel state components, including deterministic and degraded Gaussian cases, not previously characterized.

Findings

Capacity region achieved via Marton coding for deterministic components

Gaussian input distribution attains capacity in degraded Gaussian vector channels

Extensions to channels with more than two components do not generally hold

Abstract

We establish the capacity region of several classes of broadcast channels with random state in which the channel to each user is selected from two possible channel state components and the state is known only at the receivers. When the channel components are deterministic, we show that the capacity region is achieved via Marton coding. This channel model does not belong to any class of broadcast channels for which the capacity region was previously known and is useful in studying wireless communication channels when the fading state is known only at the receivers. We then establish the capacity region when the channel components are ordered, e.g., degraded. In particular we show that the capacity region for the broadcast channel with degraded Gaussian vector channel components is attained via Gaussian input distribution. Finally, we extend the results on ordered channels to two broadcast channel examples with more than two channel components, but show that these extensions do not hold in general.