Coding Schemes for a Class of Receiver Message Side Information in AWGN Broadcast Channels

TL;DR

This paper develops coding schemes and bounds for a three-receiver AWGN broadcast channel with complex side information configurations, advancing the understanding of capacity limits in these scenarios.

Contribution

It proposes inner and outer bounds for two remaining side information groups, completing capacity characterization for some configurations and narrowing gaps for others.

Findings

Inner and outer bounds coincide for group 4 in certain regions.

Capacity is established for four members of group 7.

Bounds reduce the gap for the remaining members of group 7.

Abstract

This paper considers the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests and (ii) know some of the messages requested by other receivers as side information. For this setup, all possible side information configurations have been recently classified into eight groups and the capacity of the channel has been established for six groups (Asadi et al., ISIT 2014). We propose inner and outer bounds for the two remaining groups, groups 4 and 7. A distinguishing feature of these two groups is that the weakest receiver knows the requested message of the strongest receiver as side information while the in-between receiver does not. For group 4, the inner and outer bounds coincide at certain regions. For group 7, the inner and outer bounds coincide, thereby establishing the capacity, for four members out of all eight members of the group; for the remaining four members, the proposed bounds reduce the gap between the best known inner and outer bounds.