Divide-and-conquer: Approaching the capacity of the two-pair bidirectional Gaussian relay network

TL;DR

This paper characterizes the capacity region of the two-pair bidirectional Gaussian relay network within 3 bits/sec/Hz per user by employing a divide-and-conquer strategy inspired by deterministic models.

Contribution

It introduces a divide-and-conquer relaying strategy that achieves near-capacity in Gaussian relay networks, extending deterministic model insights to practical channels.

Findings

Capacity region characterized within 3 bits/sec/Hz per user.

The divide-and-conquer strategy is optimal for deterministic models.

Achieves tight bounds for full-duplex and half-duplex modes.

Abstract

The capacity region of multi-pair bidirectional relay networks, in which a relay node facilitates the communication between multiple pairs of users, is studied. This problem is first examined in the context of the linear shift deterministic channel model. The capacity region of this network when the relay is operating at either full-duplex mode or half-duplex mode for arbitrary number of pairs is characterized. It is shown that the cut-set upper-bound is tight and the capacity region is achieved by a so called divide-and-conquer relaying strategy. The insights gained from the deterministic network are then used for the Gaussian bidirectional relay network. The strategy in the deterministic channel translates to a specific superposition of lattice codes and random Gaussian codes at the source nodes and successive interference cancelation at the receiving nodes for the Gaussian network. The achievable rate of this scheme with two pairs is analyzed and it is shown that for all channel gains it achieves to within 3 bits/sec/Hz per user of the cut-set upper-bound. Hence, the capacity region of the two-pair bidirectional Gaussian relay network to within 3 bits/sec/Hz per user is characterized.