Analog Network Coding in General SNR Regime: Performance of Network Simplification

TL;DR

This paper analyzes the performance of network simplification in layered relay networks with analog network coding, showing that using fewer relays per layer only slightly reduces the achievable rate, with bounds on the performance gap.

Contribution

It provides the first characterization of network simplification performance in general layered amplify-and-forward relay networks, offering bounds on additive and multiplicative rate gaps.

Findings

Additive gap increases no more than log(N/k)^2 bits with network simplification.

Multiplicative gap increases no more than (N/k)^2 times.

Proposes a new rate approximation scheme for simultaneous additive and multiplicative gap analysis.

Abstract

We consider a communication scenario where a source communicates with a destination over a directed layered relay network. Each relay performs analog network coding where it scales and forwards the signals received at its input. In this scenario, we address the question: What portion of the maximum end-to-end achievable rate can be maintained if only a fraction of relay nodes available at each layer are used? We consider, in particular, the Gaussian diamond network (layered network with a single layer of relay nodes) and a class of symmetric layered networks. For these networks we show that each relay layer increases the additive gap between the optimal analog network coding performance with and without network simplification (using k instead of N relays in each layer, k < N) by no more than log(N/k)^2 bits and the corresponding multiplicative gap by no more than a factor of (N/k)^2, asymptotically (in source power). To the best of our knowledge, this work offers the first characterization of the performance of network simplification in general layered amplify-and-forward relay networks. Further, unlike most of the current approximation results that attempt to bound optimal rates either within an additive gap or a multiplicative gap, our results suggest a new rate approximation scheme that allows for the simultaneous computation of additive and multiplicative gaps.