The DoF Region of the Three-Receiver MIMO Broadcast Channel with Side Information and Its Relation to Index Coding Capacity

TL;DR

This paper characterizes the degrees-of-freedom (DoF) region for a three-receiver MIMO broadcast channel with receiver message side information, providing tight bounds for all configurations and linking to index coding capacity.

Contribution

It derives the complete DoF region for all RMSI configurations in three-receiver MIMO broadcast channels, using novel schemes and enhanced channel bounds.

Findings

Established the DoF region for all 16 RMSI configurations.

Proposed new schemes exploiting null space and side information.

Linked the DoF region to the index coding capacity.

Abstract

We consider the three-receiver Gaussian multiple-input multiple-output (MIMO) broadcast channel with an arbitrary number of antennas at each of the transmitter and the receivers. We investigate the degrees-of-freedom (DoF) region of the channel when each receiver requests a private message, and may know some of the messages requested by the other receivers as receiver message side information (RMSI). We establish the DoF region of the channel for all 16 possible non-isomorphic RMSI configurations by deriving tight inner and outer bounds on the region. To derive the inner bounds, we first propose a scheme for each RMSI configuration which exploits both the null space and the side information of the receivers. We then use these schemes in conjunction with time sharing for 15 RMSI configurations, and with time sharing and two-symbol extension for the remaining one. To derive the outer bounds, we construct enhanced versions of the channel for each RMSI configuration, and upper bound their DoF region. After establishing the DoF region, in the case where all the nodes have the same number of antennas, we introduce some common properties of the DoF region, and the capacity region of the index coding problem.