On approximating Gaussian relay networks by deterministic networks

Details On approximating Gaussian relay networks by deterministic networks On approximating Gaussian relay networks by deterministic networks

2009-04-06

arxiv.org/abs/0904.0828v2

Computer Science

Information Theory

Accepted for publication in proceedings of ITW 09, Taormina, Sicily. Corrected typos, added references, changed name of networ

Scientific paper

We examine the extent to which Gaussian relay networks can be approximated by deterministic networks, and present two results, one negative and one positive. The gap between the capacities of a Gaussian relay network and a corresponding linear deterministic network can be unbounded. The key reasons are that the linear deterministic model fails to capture the phase of received signals, and there is a loss in signal strength in the reduction to a linear deterministic network. On the positive side, Gaussian relay networks are indeed well approximated by certain discrete superposition networks, where the inputs and outputs to the channels are discrete, and channel gains are signed integers. As a corollary, MIMO channels cannot be approximated by the linear deterministic model but can be by the discrete superposition model.

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