Partial Decode-Forward Relaying for the Gaussian Two-Hop Relay Network

TL;DR

This paper introduces a modified partial decode-forward scheme for the Gaussian two-hop relay network that closely approaches the multicast capacity, improving upon previous methods with a simple, low-complexity algorithm.

Contribution

It proposes a new cooperative coding scheme that achieves near-optimal multicast capacity within a small gap, with a simple linear-complexity capacity approximation algorithm.

Findings

Achieves within (1/2) log N bits of the cutset bound for general codes.

Achieves within log N bits of the cutset bound for independent relay codes.

Provides a simple linear algorithm to approximate the multicast capacity.

Abstract

The multicast capacity of the Gaussian two-hop relay network with one source, $N$ relays, and $L$ destinations is studied. It is shown that a careful modification of the partial decode--forward coding scheme, whereby the relays cooperate through degraded sets of message parts, achieves the cutset upper bound within $(1/2)\log N$ bits regardless of the channel gains and power constraints. This scheme improves upon a previous scheme by Chern and Ozgur, which is also based on partial decode--forward yet has an unbounded gap from the cutset bound for $L \ge 2$ destinations. When specialized to independent codes among relays, the proposed scheme achieves within $\log N$ bits from the cutset bound. The computation of this relaxation involves evaluating mutual information across $L(N+1)$ cuts out of the total $L 2^N$ possible cuts, providing a very simple linear-complexity algorithm to approximate the single-source multicast capacity of the Gaussian two-hop relay network.