Optimal Coding Schemes for the Three-Receiver AWGN Broadcast Channel with Receiver Message Side Information

TL;DR

This paper characterizes the capacity regions of a three-receiver AWGN broadcast channel with various message side information configurations, improving bounds and establishing capacity for many cases.

Contribution

It classifies all side information configurations into groups, constructs transmission schemes, and derives bounds that establish capacity regions for most configurations.

Findings

Capacity region established for 52 of 64 configurations.

Bounds tightened for multiple configuration groups.

Capacity established for four specific group members.

Abstract

This paper investigates the capacity region of the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests and (ii) may know some of the messages requested by other receivers as side information. We first classify all 64 possible side information configurations into eight groups, each consisting of eight members. We next construct transmission schemes, and derive new inner and outer bounds for the groups. This establishes the capacity region for 52 out of 64 possible side information configurations. For six groups (i.e., groups 1, 2, 3, 5, 6, and 8 in our terminology), we establish the capacity region for all their members, and show that it tightens both the best known inner and outer bounds. For group 4, our inner and outer bounds tighten the best known inner bound and/or outer bound for all the group members. Moreover, our bounds coincide at certain regions, which can be characterized by two thresholds. For group 7, our inner and outer bounds coincide for four members, thereby establishing the capacity region. For the remaining four members, our bounds tighten both the best known inner and outer bounds.