Capacity region of the deterministic multi-pair bi-directional relay network

TL;DR

This paper characterizes the capacity region of a deterministic multi-pair bidirectional relay network, showing that a simple equation-forwarding strategy achieves the cut-set bound in both full-duplex and half-duplex modes.

Contribution

It extends the understanding of relay networks by providing a complete capacity region characterization for the multi-pair case under deterministic modeling, using a straightforward strategy.

Findings

Cut-set bound is tight for the network.

Equation-forwarding strategy achieves capacity.

Capacity region characterized for both full-duplex and half-duplex modes.

Abstract

In this paper we study the capacity region of the multi-pair bidirectional (or two-way) wireless relay network, in which a relay node facilitates the communication between multiple pairs of users. This network is a generalization of the well known bidirectional relay channel, where we have only one pair of users. We examine this problem in the context of the deterministic channel interaction model, which eliminates the channel noise and allows us to focus on the interaction between signals. We characterize the capacity region of this network when the relay is operating at either full-duplex mode or half-duplex mode (with non adaptive listen-transmit scheduling). In both cases we show that the cut-set upper bound is tight and, quite interestingly, the capacity region is achieved by a simple equation-forwarding strategy.