Network Simplification for Secure AF Relaying

TL;DR

This paper analyzes how much secure communication rate can be preserved in layered relay networks when only a subset of relays are used, providing bounds on performance gaps and introducing the first such characterization under eavesdropping conditions.

Contribution

It offers the first analysis of network simplification effects on secure AF relay networks with eavesdroppers, establishing bounds on performance gaps.

Findings

Additive gap grows logarithmically with N/k and L.

Multiplicative gap grows quadratically with N/k and L.

Performance bounds are asymptotic in source power.

Abstract

We consider a class of Gaussian layered networks where a source communicates with a destination through L intermediate relay layers with N nodes in each layer in the presence of a single eavesdropper which can overhear the transmissions of the nodes in the last layer. For such networks we address the question: what fraction of maximum secure achievable rate can be maintained if only a fraction of available relay nodes are used in each layer? In particular, we provide upper bounds on additive and multiplicative gaps between the optimal secure AF when all N relays in each layer are used and when only k, 1 <= k < N, relays are used in each layer. We show that asymptotically (in source power), the additive gap increases at most logarithmically with ratio N/k and L, and the corresponding multiplicative gap increases at most quadratically with ratio N/k and L. To the best of our knowledge, this work offers the first characterization of the performance of network simplification in layered amplify-and-forward relay networks in the presence of an eavesdropper.