1,542 research outputs found
The Approximate Capacity of the Gaussian N-Relay Diamond Network
We consider the Gaussian "diamond" or parallel relay network, in which a
source node transmits a message to a destination node with the help of N
relays. Even for the symmetric setting, in which the channel gains to the
relays are identical and the channel gains from the relays are identical, the
capacity of this channel is unknown in general. The best known capacity
approximation is up to an additive gap of order N bits and up to a
multiplicative gap of order N^2, with both gaps independent of the channel
gains.
In this paper, we approximate the capacity of the symmetric Gaussian N-relay
diamond network up to an additive gap of 1.8 bits and up to a multiplicative
gap of a factor 14. Both gaps are independent of the channel gains and, unlike
the best previously known result, are also independent of the number of relays
N in the network. Achievability is based on bursty amplify-and-forward, showing
that this simple scheme is uniformly approximately optimal, both in the
low-rate as well as in the high-rate regimes. The upper bound on capacity is
based on a careful evaluation of the cut-set bound. We also present
approximation results for the asymmetric Gaussian N-relay diamond network. In
particular, we show that bursty amplify-and-forward combined with optimal relay
selection achieves a rate within a factor O(log^4(N)) of capacity with
pre-constant in the order notation independent of the channel gains.Comment: 23 pages, to appear in IEEE Transactions on Information Theor
Gaussian 1-2-1 Networks: Capacity Results for mmWave Communications
This paper proposes a new model for wireless relay networks referred to as
"1-2-1 network", where two nodes can communicate only if they point "beams" at
each other, while if they do not point beams at each other, no signal can be
exchanged or interference can be generated. This model is motivated by
millimeter wave communications where, due to the high path loss, a link between
two nodes can exist only if beamforming gain at both sides is established,
while in the absence of beamforming gain the signal is received well below the
thermal noise floor. The main result in this paper is that the 1-2-1 network
capacity can be approximated by routing information along at most paths,
where is the number of relays connecting a source and a destination through
an arbitrary topology
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
Wireless Network Simplification: the Gaussian N-Relay Diamond Network
We consider the Gaussian N-relay diamond network, where a source wants to
communicate to a destination node through a layer of N-relay nodes. We
investigate the following question: what fraction of the capacity can we
maintain by using only k out of the N available relays? We show that
independent of the channel configurations and the operating SNR, we can always
find a subset of k relays which alone provide a rate (kC/(k+1))-G, where C is
the information theoretic cutset upper bound on the capacity of the whole
network and G is a constant that depends only on N and k (logarithmic in N and
linear in k). In particular, for k = 1, this means that half of the capacity of
any N-relay diamond network can be approximately achieved by routing
information over a single relay. We also show that this fraction is tight:
there are configurations of the N-relay diamond network where every subset of k
relays alone can at most provide approximately a fraction k/(k+1) of the total
capacity. These high-capacity k-relay subnetworks can be also discovered
efficiently. We propose an algorithm that computes a constant gap approximation
to the capacity of the Gaussian N-relay diamond network in O(N log N) running
time and discovers a high-capacity k-relay subnetwork in O(kN) running time.
This result also provides a new approximation to the capacity of the Gaussian
N-relay diamond network which is hybrid in nature: it has both multiplicative
and additive gaps. In the intermediate SNR regime, this hybrid approximation is
tighter than existing purely additive or purely multiplicative approximations
to the capacity of this network.Comment: Submitted to Transactions on Information Theory in October 2012. The
new version includes discussions on the algorithmic complexity of discovering
a high-capacity subnetwork and on the performance of amplify-and-forwar
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 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 active
states (only out of the 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 -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
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
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