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We consider a class of Gaussian layered networks where a source communicateswith a destination through L intermediate relay layers with N nodes in eachlayer in the presence of a single eavesdropper which can overhear thetransmissions of the nodes in the last layer. For such networks we address thequestion: what fraction of maximum secure achievable rate can be maintained ifonly a fraction of available relay nodes are used in each layer? In particular,we provide upper bounds on additive and multiplicative gaps between the optimalsecure 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, andthe corresponding multiplicative gap increases at most quadratically with ratioN/k and L. To the best of our knowledge, this work offers the firstcharacterization of the performance of network simplification in layeredamplify-and-forward relay networks in the presence of an eavesdropper.

Network Simplification for Secure AF Relaying