Wireless Network Information Flow: A Deterministic Approach

In a wireless network with a single source and a single destination and an arbitrary number of relay nodes, what is the maximum rate of information flow achievable? We make progress on this long standing problem through a two-step approach. First we propose a deterministic channel model which captures the key wireless properties of signal strength, broadcast and superposition. We obtain an exact characterization of the capacity of a network with nodes connected by such deterministic channels. This result is a natural generalization of the celebrated max-flow min-cut theorem for wired networks. Second, we use the insights obtained from the deterministic analysis to design a new quantize-map-and-forward scheme for Gaussian networks. In this scheme, each relay quantizes the received signal at the noise level and maps it to a random Gaussian codeword for forwarding, and the final destination decodes the source's message based on the received signal. We show that, in contrast to existing schemes, this scheme can achieve the cut-set upper bound to within a gap which is independent of the channel parameters. In the case of the relay channel with a single relay as well as the two-relay Gaussian diamond network, the gap is 1 bit/s/Hz. Moreover, the scheme is universal in the sense that the relays need no knowledge of the values of the channel parameters to (approximately) achieve the rate supportable by the network. We also present extensions of the results to multicast networks, half-duplex networks and ergodic networks.Comment: To appear in IEEE transactions on Information Theory, Vol 57, No 4, April 201

Asymptotic Capacity of Large Relay Networks with Conferencing Links

In this correspondence, we consider a half-duplex large relay network, which consists of one source-destination pair and $N$ relay nodes, each of which is connected with a subset of the other relays via signal-to-noise ratio (SNR)-limited out-of-band conferencing links. The asymptotic achievable rates of two basic relaying schemes with the "$p$-portion" conferencing strategy are studied: For the decode-and-forward (DF) scheme, we prove that the DF rate scales as $\mathcal{O} (\log (N))$; for the amplify-and-forward (AF) scheme, we prove that it asymptotically achieves the capacity upper bound in some interesting scenarios as $N$ goes to infinity.Comment: submitted to IEEE Transactions on Communication

The Approximate Optimality of Simple Schedules for Half-Duplex Multi-Relay Networks

In ISIT'12 Brahma, \"{O}zg\"{u}r and Fragouli conjectured that in a half-duplex diamond relay network (a Gaussian noise network without a direct source-destination link and with $N$ non-interfering relays) an approximately optimal relay scheduling (achieving the cut-set upper bound to within a constant gap uniformly over all channel gains) exists with at most $N+1$ active states (only $N+1$ out of the $2^N$ possible relay listen-transmit configurations have a strictly positive probability). Such relay scheduling policies are said to be simple. In ITW'13 we conjectured that simple relay policies are optimal for any half-duplex Gaussian multi-relay network, that is, simple schedules are not a consequence of the diamond network's sparse topology. In this paper we formally prove the conjecture beyond Gaussian networks. In particular, for any memoryless half-duplex $N$-relay network with independent noises and for which independent inputs are approximately optimal in the cut-set upper bound, an optimal schedule exists with at most $N+1$ active states. The key step of our proof is to write the minimum of a submodular function by means of its Lov\'{a}sz extension and use the greedy algorithm for submodular polyhedra to highlight structural properties of the optimal solution. This, together with the saddle-point property of min-max problems and the existence of optimal basic feasible solutions in linear programs, proves the claim.Comment: Submitted to IEEE Information Theory Workshop (ITW) 201