6,724 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
Asymptotic Capacity of Large Fading Relay Networks with Random Node Failures
To understand the network response to large-scale physical attacks, we
investigate the asymptotic capacity of a half-duplex fading relay network with
random node failures when the number of relays is infinitely large. In this
paper, a simplified independent attack model is assumed where each relay node
fails with a certain probability. The noncoherent relaying scheme is
considered, which corresponds to the case of zero forward-link channel state
information (CSI) at the relays. Accordingly, the whole relay network can be
shown equivalent to a Rayleigh fading channel, where we derive the
-outage capacity upper bound according to the multiple access (MAC)
cut-set, and the -outage achievable rates for both the
amplify-and-forward (AF) and decode-and-forward (DF) strategies. Furthermore,
we show that the DF strategy is asymptotically optimal as the outage
probability goes to zero, with the AF strategy strictly suboptimal
over all signal to noise ratio (SNR) regimes. Regarding the rate loss due to
random attacks, the AF strategy suffers a less portion of rate loss than the DF
strategy in the high SNR regime, while the DF strategy demonstrates more robust
performance in the low SNR regime.Comment: 24 pages, 5 figures, submitted to IEEE Transactions on Communication
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
Efficiently Finding Simple Schedules in Gaussian Half-Duplex Relay Line Networks
The problem of operating a Gaussian Half-Duplex (HD) relay network optimally
is challenging due to the exponential number of listen/transmit network states
that need to be considered. Recent results have shown that, for the class of
Gaussian HD networks with N relays, there always exists a simple schedule,
i.e., with at most N +1 active states, that is sufficient for approximate
(i.e., up to a constant gap) capacity characterization. This paper investigates
how to efficiently find such a simple schedule over line networks. Towards this
end, a polynomial-time algorithm is designed and proved to output a simple
schedule that achieves the approximate capacity. The key ingredient of the
algorithm is to leverage similarities between network states in HD and edge
coloring in a graph. It is also shown that the algorithm allows to derive a
closed-form expression for the approximate capacity of the Gaussian line
network that can be evaluated distributively and in linear time. Additionally,
it is shown using this closed-form that the problem of Half-Duplex routing is
NP-Hard.Comment: A short version of this paper was submitted to ISIT 201
Computation Alignment: Capacity Approximation without Noise Accumulation
Consider several source nodes communicating across a wireless network to a
destination node with the help of several layers of relay nodes. Recent work by
Avestimehr et al. has approximated the capacity of this network up to an
additive gap. The communication scheme achieving this capacity approximation is
based on compress-and-forward, resulting in noise accumulation as the messages
traverse the network. As a consequence, the approximation gap increases
linearly with the network depth.
This paper develops a computation alignment strategy that can approach the
capacity of a class of layered, time-varying wireless relay networks up to an
approximation gap that is independent of the network depth. This strategy is
based on the compute-and-forward framework, which enables relays to decode
deterministic functions of the transmitted messages. Alone, compute-and-forward
is insufficient to approach the capacity as it incurs a penalty for
approximating the wireless channel with complex-valued coefficients by a
channel with integer coefficients. Here, this penalty is circumvented by
carefully matching channel realizations across time slots to create
integer-valued effective channels that are well-suited to compute-and-forward.
Unlike prior constant gap results, the approximation gap obtained in this paper
also depends closely on the fading statistics, which are assumed to be i.i.d.
Rayleigh.Comment: 36 pages, to appear in IEEE Transactions on Information Theor
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