5,703 research outputs found
Quantum network communication -- the butterfly and beyond
We study the k-pair communication problem for quantum information in networks
of quantum channels. We consider the asymptotic rates of high fidelity quantum
communication between specific sender-receiver pairs. Four scenarios of
classical communication assistance (none, forward, backward, and two-way) are
considered. (i) We obtain outer and inner bounds of the achievable rate regions
in the most general directed networks. (ii) For two particular networks
(including the butterfly network) routing is proved optimal, and the free
assisting classical communication can at best be used to modify the directions
of quantum channels in the network. Consequently, the achievable rate regions
are given by counting edge avoiding paths, and precise achievable rate regions
in all four assisting scenarios can be obtained. (iii) Optimality of routing
can also be proved in classes of networks. The first class consists of directed
unassisted networks in which (1) the receivers are information sinks, (2) the
maximum distance from senders to receivers is small, and (3) a certain type of
4-cycles are absent, but without further constraints (such as on the number of
communicating and intermediate parties). The second class consists of arbitrary
backward-assisted networks with 2 sender-receiver pairs. (iv) Beyond the k-pair
communication problem, observations are made on quantum multicasting and a
static version of network communication related to the entanglement of
assistance.Comment: 15 pages, 17 figures. Final versio
OutFlank Routing: Increasing Throughput in Toroidal Interconnection Networks
We present a new, deadlock-free, routing scheme for toroidal interconnection
networks, called OutFlank Routing (OFR). OFR is an adaptive strategy which
exploits non-minimal links, both in the source and in the destination nodes.
When minimal links are congested, OFR deroutes packets to carefully chosen
intermediate destinations, in order to obtain travel paths which are only an
additive constant longer than the shortest ones. Since routing performance is
very sensitive to changes in the traffic model or in the router parameters, an
accurate discrete-event simulator of the toroidal network has been developed to
empirically validate OFR, by comparing it against other relevant routing
strategies, over a range of typical real-world traffic patterns. On the
16x16x16 (4096 nodes) simulated network OFR exhibits improvements of the
maximum sustained throughput between 14% and 114%, with respect to Adaptive
Bubble Routing.Comment: 9 pages, 5 figures, to be presented at ICPADS 201
General Scheme for Perfect Quantum Network Coding with Free Classical Communication
This paper considers the problem of efficiently transmitting quantum states
through a network. It has been known for some time that without additional
assumptions it is impossible to achieve this task perfectly in general --
indeed, it is impossible even for the simple butterfly network. As additional
resource we allow free classical communication between any pair of network
nodes. It is shown that perfect quantum network coding is achievable in this
model whenever classical network coding is possible over the same network when
replacing all quantum capacities by classical capacities. More precisely, it is
proved that perfect quantum network coding using free classical communication
is possible over a network with source-target pairs if there exists a
classical linear (or even vector linear) coding scheme over a finite ring. Our
proof is constructive in that we give explicit quantum coding operations for
each network node. This paper also gives an upper bound on the number of
classical communication required in terms of , the maximal fan-in of any
network node, and the size of the network.Comment: 12 pages, 2 figures, generalizes some of the results in
arXiv:0902.1299 to the k-pair problem and codes over rings. Appeared in the
Proceedings of the 36th International Colloquium on Automata, Languages and
Programming (ICALP'09), LNCS 5555, pp. 622-633, 200
Path Gain Algebraic Formulation for the Scalar Linear Network Coding Problem
In the algebraic view, the solution to a network coding problem is seen as a
variety specified by a system of polynomial equations typically derived by
using edge-to-edge gains as variables. The output from each sink is equated to
its demand to obtain polynomial equations. In this work, we propose a method to
derive the polynomial equations using source-to-sink path gains as the
variables. In the path gain formulation, we show that linear and quadratic
equations suffice; therefore, network coding becomes equivalent to a system of
polynomial equations of maximum degree 2. We present algorithms for generating
the equations in the path gains and for converting path gain solutions to
edge-to-edge gain solutions. Because of the low degree, simplification is
readily possible for the system of equations obtained using path gains. Using
small-sized network coding problems, we show that the path gain approach
results in simpler equations and determines solvability of the problem in
certain cases. On a larger network (with 87 nodes and 161 edges), we show how
the path gain approach continues to provide deterministic solutions to some
network coding problems.Comment: 12 pages, 6 figures. Accepted for publication in IEEE Transactions on
Information Theory (May 2010
Network Coding for Computing: Cut-Set Bounds
The following \textit{network computing} problem is considered. Source nodes
in a directed acyclic network generate independent messages and a single
receiver node computes a target function of the messages. The objective is
to maximize the average number of times can be computed per network usage,
i.e., the ``computing capacity''. The \textit{network coding} problem for a
single-receiver network is a special case of the network computing problem in
which all of the source messages must be reproduced at the receiver. For
network coding with a single receiver, routing is known to achieve the capacity
by achieving the network \textit{min-cut} upper bound. We extend the definition
of min-cut to the network computing problem and show that the min-cut is still
an upper bound on the maximum achievable rate and is tight for computing (using
coding) any target function in multi-edge tree networks and for computing
linear target functions in any network. We also study the bound's tightness for
different classes of target functions. In particular, we give a lower bound on
the computing capacity in terms of the Steiner tree packing number and a
different bound for symmetric functions. We also show that for certain networks
and target functions, the computing capacity can be less than an arbitrarily
small fraction of the min-cut bound.Comment: Submitted to the IEEE Transactions on Information Theory (Special
Issue on Facets of Coding Theory: from Algorithms to Networks); Revised on
Aug 9, 201
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