Improved Capacity Approximations for Gaussian Relay Networks

TL;DR

This paper demonstrates that by adjusting relay quantization levels based on network size, the capacity gap in Gaussian relay networks can be reduced from linear to logarithmic, improving efficiency over traditional methods.

Contribution

It introduces a novel quantization strategy that decreases resolution with network size, significantly reducing the capacity gap in layered relay networks.

Findings

Capacity gap becomes logarithmic in network size with the new quantization method.

Traditional noise-level quantization is suboptimal for large networks.

The approach applies to layered, time-varying wireless relay networks.

Abstract

Consider a Gaussian relay network where a number of sources communicate to a destination with the help of several layers of relays. Recent work has shown that a compress-and-forward based strategy at the relays can achieve the capacity of this network within an additive gap. In this strategy, the relays quantize their observations at the noise level and map it to a random Gaussian codebook. The resultant capacity gap is independent of the SNR's of the channels in the network but linear in the total number of nodes. In this paper, we show that if the relays quantize their signals at a resolution decreasing with the number of nodes in the network, the additive gap to capacity can be made logarithmic in the number of nodes for a class of layered, time-varying wireless relay networks. This suggests that the rule-of-thumb to quantize the received signals at the noise level used for compress-and-forward in the current literature can be highly suboptimal.