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Network Information Theory: Multi-Access and Broadcast Channels

Module by: Adan Galvan

Summary: This is a brief summary of what has been known about network information theory. It covers multiaccess and broadcast channels, in an attemp to summarize about thwo dozen scattered papers in both subjects.

Introduction

In this summary we dsicuss two types of multiuser channels: the multi-access channel and broadcast channel. In the former many senders wish to send messages to one receiver, and in the letter on sender wishes to send messages to many receivers. We are specifically interested in a survey of tools that are used.

Information-Theoretic Tools

The Slepian-Wolf binning technique

First introduced by Slepian and Wolf in their landmark paper to show the capacity of source coding with side information. Also used by Gel'fand-Pinsker to show the capacity of channel coding with side information.

The latter was extended to include the broadcast channel by Marton and El Gamal.Possibly also used earlier by Bergmans and Gallager in 1, 2, 11.

Interestingly also used to show an achievable region for interference channels by Carleul in 4. Probably also by Han.

theorem 1: Slepian-Wolf

Let (X,Y) be iid r.v.'s from a joint distribution. Recall the notion of joint typically. The achievable region is given by: R 1 ≥HYX R 1 H Y X

Proof

Example

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