Analog network coding in general SNR regime: Performance of a greedy scheme

TL;DR

This paper introduces a greedy scheme to compute lower bounds on the maximum achievable rate with analog network coding in layered relay networks, extending analysis beyond previous assumptions and providing exact results for certain network types.

Contribution

It presents a novel greedy algorithm for lower bounding the optimal analog network coding rate in general layered networks, including the first exact characterization for Gaussian N-relay diamond networks.

Findings

The scheme computes achievable rates within a constant gap of the cut-set bound.

It provides the first exact rate characterization for Gaussian N-relay diamond networks.

The method extends analysis to broader network scenarios beyond previous assumptions.

Abstract

The problem of maximum rate achievable with analog network coding for a unicast communication over a layered relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been considered under certain assumptions on per node scaling factor and received SNR. Previously, we established a result that allows us to characterize the optimal performance of analog network coding in network scenarios beyond those that can be analyzed using the approaches based on such assumptions. The key contribution of this work is a scheme to greedily compute a lower bound to the optimal rate achievable with analog network coding in the general layered networks. This scheme allows for exact computation of the optimal achievable rates in a wider class of layered networks than those that can be addressed using existing approaches. For the specific case of Gaussian N-relay diamond network, to the best of our knowledge, the proposed scheme provides the first exact characterization of the optimal rate achievable with analog network coding. Further, for general layered networks, our scheme allows us to compute optimal rates within a constant gap from the cut-set upper bound asymptotically in the source power.