1,044 research outputs found
The Deterministic Multicast Capacity of 4-Node Relay Networks
In this paper, we completely characterize the deterministic capacity region
of a four-node relay network with no direct links between the nodes, where each
node communicates with the three other nodes via a relay. Towards this end, we
develop an upper bound on the deterministic capacity region, based on the
notion of a one-sided genie. To establish achievability, we use the detour
schemes that achieve the upper bound by routing specific bits via indirect
paths instead of sending them directly.Comment: 5 pages, 2 figures, accepted at ISIT'1
Near-optimal quantization and linear network coding for relay networks
We introduce a discrete network corresponding to any Gaussian wireless
network that is obtained by simply quantizing the received signals and
restricting the transmitted signals to a finite precision. Since signals in the
discrete network are obtained from those of a Gaussian network, the Gaussian
network can be operated on the quantization-based digital interface defined by
the discrete network. We prove that this digital interface is near-optimal for
Gaussian relay networks and the capacities of the Gaussian and the discrete
networks are within a bounded gap of O(M^2) bits, where M is the number of
nodes.
We prove that any near-optimal coding strategy for the discrete network can
be naturally transformed into a near-optimal coding strategy for the Gaussian
network merely by quantization. We exploit this by designing a linear coding
strategy for the case of layered discrete relay networks. The linear coding
strategy is near-optimal for Gaussian and discrete networks and achieves rates
within O(M^2) bits of the capacity, independent of channel gains or SNR. The
linear code is robust and the relays need not know the channel gains. The
transmit and receive signals at all relays are simply quantized to binary
tuples of the same length . The linear network code requires all the relay
nodes to collect the received binary tuples into a long binary vector and apply
a linear transformation on the long vector. The resulting binary vector is
split into smaller binary tuples for transmission by the relays. The
quantization requirements of the linear network code are completely defined by
the parameter , which also determines the resolution of the
analog-to-digital and digital-to-analog convertors for operating the network
within a bounded gap of the network's capacity. The linear network code
explicitly connects network coding for wireline networks with codes for
Gaussian networks.Comment: Submitted to Transactions on Information Theor
Slepian-Wolf Coding Over Cooperative Relay Networks
This paper deals with the problem of multicasting a set of discrete
memoryless correlated sources (DMCS) over a cooperative relay network.
Necessary conditions with cut-set interpretation are presented. A \emph{Joint
source-Wyner-Ziv encoding/sliding window decoding} scheme is proposed, in which
decoding at each receiver is done with respect to an ordered partition of other
nodes. For each ordered partition a set of feasibility constraints is derived.
Then, utilizing the sub-modular property of the entropy function and a novel
geometrical approach, the results of different ordered partitions are
consolidated, which lead to sufficient conditions for our problem. The proposed
scheme achieves operational separation between source coding and channel
coding. It is shown that sufficient conditions are indeed necessary conditions
in two special cooperative networks, namely, Aref network and finite-field
deterministic network. Also, in Gaussian cooperative networks, it is shown that
reliable transmission of all DMCS whose Slepian-Wolf region intersects the
cut-set bound region within a constant number of bits, is feasible. In
particular, all results of the paper are specialized to obtain an achievable
rate region for cooperative relay networks which includes relay networks and
two-way relay networks.Comment: IEEE Transactions on Information Theory, accepte
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
A digital interface for Gaussian relay and interference networks: Lifting codes from the discrete superposition model
For every Gaussian network, there exists a corresponding deterministic
network called the discrete superposition network. We show that this discrete
superposition network provides a near-optimal digital interface for operating a
class consisting of many Gaussian networks in the sense that any code for the
discrete superposition network can be naturally lifted to a corresponding code
for the Gaussian network, while achieving a rate that is no more than a
constant number of bits lesser than the rate it achieves for the discrete
superposition network. This constant depends only on the number of nodes in the
network and not on the channel gains or SNR. Moreover the capacities of the two
networks are within a constant of each other, again independent of channel
gains and SNR. We show that the class of Gaussian networks for which this
interface property holds includes relay networks with a single
source-destination pair, interference networks, multicast networks, and the
counterparts of these networks with multiple transmit and receive antennas.
The code for the Gaussian relay network can be obtained from any code for the
discrete superposition network simply by pruning it. This lifting scheme
establishes that the superposition model can indeed potentially serve as a
strong surrogate for designing codes for Gaussian relay networks.
We present similar results for the K x K Gaussian interference network, MIMO
Gaussian interference networks, MIMO Gaussian relay networks, and multicast
networks, with the constant gap depending additionally on the number of
antennas in case of MIMO networks.Comment: Final versio
Wireless Network Information Flow
We present an achievable rate for general deterministic relay networks, with
broadcasting at the transmitters and interference at the receivers. In
particular we show that if the optimizing distribution for the
information-theoretic cut-set bound is a product distribution, then we have a
complete characterization of the achievable rates for such networks. For linear
deterministic finite-field models discussed in a companion paper [3], this is
indeed the case, and we have a generalization of the celebrated max-flow
min-cut theorem for such a network.Comment: - Corrected Typo
Distributed Decode-Forward for Relay Networks
A new coding scheme for general N-node relay networks is presented for
unicast, multicast, and broadcast. The proposed distributed decode-forward
scheme combines and generalizes Marton coding for single-hop broadcast channels
and the Cover-El Gamal partial decode-forward coding scheme for 3-node relay
channels. The key idea of the scheme is to precode all the codewords of the
entire network at the source by multicoding over multiple blocks. This encoding
step allows these codewords to carry partial information of the messages
implicitly without complicated rate splitting and routing. This partial
information is then recovered at the relay nodes and forwarded further. For
N-node Gaussian unicast, multicast, and broadcast relay networks, the scheme
achieves within 0.5N bits from the cutset bound and thus from the capacity
(region), regardless of the network topology, channel gains, or power
constraints. Roughly speaking, distributed decode-forward is dual to noisy
network coding, which generalized compress-forward to unicast, multicast, and
multiple access relay networks.Comment: 32 pages, 5 figures, submitted to the IEEE Transactions on
Information Theor
A Deterministic Polynomial--Time Algorithm for Constructing a Multicast Coding Scheme for Linear Deterministic Relay Networks
We propose a new way to construct a multicast coding scheme for linear
deterministic relay networks. Our construction can be regarded as a
generalization of the well-known multicast network coding scheme of Jaggi et
al. to linear deterministic relay networks and is based on the notion of flow
for a unicast session that was introduced by the authors in earlier work. We
present randomized and deterministic polynomial--time versions of our algorithm
and show that for a network with destinations, our deterministic algorithm
can achieve the capacity in uses of the
network.Comment: 12 pages, 2 figures, submitted to CISS 201
Using Network Coding to Achieve the Capacity of Deterministic Relay Networks with Relay Messages
In this paper, we derive the capacity of the deterministic relay networks
with relay messages. We consider a network which consists of five nodes, four
of which can only communicate via the fifth one. However, the fifth node is not
merely a relay as it may exchange private messages with the other network
nodes. First, we develop an upper bound on the capacity region based on the
notion of a single sided genie. In the course of the achievability proof, we
also derive the deterministic capacity of a 4-user relay network (without
private messages at the relay). The capacity achieving schemes use a
combination of two network coding techniques: the Simple Ordering Scheme (SOS)
and Detour Schemes (DS). In the SOS, we order the transmitted bits at each user
such that the bi-directional messages will be received at the same channel
level at the relay, while the basic idea behind the DS is that some parts of
the message follow an indirect path to their respective destinations. This
paper, therefore, serves to show that user cooperation and network coding can
enhance throughput, even when the users are not directly connected to each
other.Comment: 12 pages, 5 figures, submitted to IEEE JSAC Network codin
Classes of Delay-Independent Multimessage Multicast Networks with Zero-Delay Nodes
In a network, a node is said to incur a delay if its encoding of each
transmitted symbol involves only its received symbols obtained before the time
slot in which the transmitted symbol is sent (hence the transmitted symbol sent
in a time slot cannot depend on the received symbol obtained in the same time
slot). A node is said to incur no delay if its received symbol obtained in a
time slot is available for encoding its transmitted symbol sent in the same
time slot. Under the classical model, every node in the network incurs a delay.
In this paper, we investigate the multimessage multicast network (MMN) under a
generalized-delay model which allows some nodes to incur no delay. We obtain
the capacity regions for three classes of MMNs with zero-delay nodes, namely
the deterministic network dominated by product distribution, the MMN consisting
of independent DMCs and the wireless erasure network. In addition, we show that
for any MMN belonging to one of the above three classes, the set of achievable
rate tuples under the generalized-delay model and under the classical model are
the same, which implies that the set of achievable rate tuples for the MMN does
not depend on the delay amounts incurred by the nodes in the network.Comment: 32 pages. Submitted to IEEE Transactions on Information Theor
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