27,287 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
Degraded Broadcast Diamond Channels with Non-Causal State Information at the Source
A state-dependent degraded broadcast diamond channel is studied where the
source-to-relays cut is modeled with two noiseless, finite-capacity digital
links with a degraded broadcasting structure, while the relays-to-destination
cut is a general multiple access channel controlled by a random state. It is
assumed that the source has non-causal channel state information and the relays
have no state information. Under this model, first, the capacity is
characterized for the case where the destination has state information, i.e.,
has access to the state sequence. It is demonstrated that in this case, a joint
message and state transmission scheme via binning is optimal. Next, the case
where the destination does not have state information, i.e., the case with
state information at the source only, is considered. For this scenario, lower
and upper bounds on the capacity are derived for the general discrete
memoryless model. Achievable rates are then computed for the case in which the
relays-to-destination cut is affected by an additive Gaussian state. Numerical
results are provided that illuminate the performance advantages that can be
accrued by leveraging non-causal state information at the source.Comment: Submitted to IEEE Transactions on Information Theory, Feb. 201
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
- …