85 research outputs found
On Approximating the Sum-Rate for Multiple-Unicasts
We study upper bounds on the sum-rate of multiple-unicasts. We approximate
the Generalized Network Sharing Bound (GNS cut) of the multiple-unicasts
network coding problem with independent sources. Our approximation
algorithm runs in polynomial time and yields an upper bound on the joint source
entropy rate, which is within an factor from the GNS cut. It
further yields a vector-linear network code that achieves joint source entropy
rate within an factor from the GNS cut, but \emph{not} with
independent sources: the code induces a correlation pattern among the sources.
Our second contribution is establishing a separation result for vector-linear
network codes: for any given field there exist networks for which
the optimum sum-rate supported by vector-linear codes over for
independent sources can be multiplicatively separated by a factor of
, for any constant , from the optimum joint entropy
rate supported by a code that allows correlation between sources. Finally, we
establish a similar separation result for the asymmetric optimum vector-linear
sum-rates achieved over two distinct fields and
for independent sources, revealing that the choice of field
can heavily impact the performance of a linear network code.Comment: 10 pages; Shorter version appeared at ISIT (International Symposium
on Information Theory) 2015; some typos correcte
Distributed design of network codes for wireless multiple unicasts
Previous results on network coding for low-power
wireless transmissions of multiple unicasts rely on opportunistic
coding or centralized optimization to reduce the power
consumption. This paper proposes a distributed strategy for
reducing the power consumption in a network coded wireless
network with multiple unicasts. We apply a simple network
coding strategy called âreverse carpooling,â which uses only
XOR and forwarding operations. In this paper, we use the
rectangular grid as a simple network model and attempt to
increase network coding opportunities without the overhead
required for centralized design or coordination. The proposed
technique designates âreverse carpooling linesâ analogous to
a collection of bus routes in a crowded city. Each individual
unicast then chooses a route from its source to its destination
independently but in a manner that maximizes the fraction
of its path spent on reverse carpooling lines. Intermediate
nodes apply reverse carpooling opportunistically along these
routes. Our network optimization attempts to choose the reverse
carpooling lines in a manner that maximizes the expected power
savings with respect to the random choice of sources and sinks
Precoding-Based Network Alignment For Three Unicast Sessions
We consider the problem of network coding across three unicast sessions over
a directed acyclic graph, where each sender and the receiver is connected to
the network via a single edge of unit capacity. We consider a network model in
which the middle of the network only performs random linear network coding, and
restrict our approaches to precoding-based linear schemes, where the senders
use precoding matrices to encode source symbols. We adapt a precoding-based
interference alignment technique, originally developed for the wireless
interference channel, to construct a precoding-based linear scheme, which we
refer to as as a {\em precoding-based network alignment scheme (PBNA)}. A
primary difference between this setting and the wireless interference channel
is that the network topology can introduce dependencies between elements of the
transfer matrix, which we refer to as coupling relations, and can potentially
affect the achievable rate of PBNA. We identify all possible such coupling
relations, and interpret these coupling relations in terms of network topology
and present polynomial-time algorithms to check the presence of these coupling
relations. Finally, we show that, depending on the coupling relations present
in the network, the optimal symmetric rate achieved by precoding-based linear
scheme can take only three possible values, all of which can be achieved by
PBNA.Comment: arXiv admin note: text overlap with arXiv:1202.340
A Linear Network Code Construction for General Integer Connections Based on the Constraint Satisfaction Problem
The problem of finding network codes for general connections is inherently
difficult in capacity constrained networks. Resource minimization for general
connections with network coding is further complicated. Existing methods for
identifying solutions mainly rely on highly restricted classes of network
codes, and are almost all centralized. In this paper, we introduce linear
network mixing coefficients for code constructions of general connections that
generalize random linear network coding (RLNC) for multicast connections. For
such code constructions, we pose the problem of cost minimization for the
subgraph involved in the coding solution and relate this minimization to a
path-based Constraint Satisfaction Problem (CSP) and an edge-based CSP. While
CSPs are NP-complete in general, we present a path-based probabilistic
distributed algorithm and an edge-based probabilistic distributed algorithm
with almost sure convergence in finite time by applying Communication Free
Learning (CFL). Our approach allows fairly general coding across flows,
guarantees no greater cost than routing, and shows a possible distributed
implementation. Numerical results illustrate the performance improvement of our
approach over existing methods.Comment: submitted to TON (conference version published at IEEE GLOBECOM 2015
A Linear Network Code Construction for General Integer Connections Based on the Constraint Satisfaction Problem
The problem of finding network codes for general connections is inherently difficult. Resource minimization for general connections with network coding is further complicated. The existing solutions mainly rely on very restricted classes of network codes, and are almost all centralized. In this paper, we introduce linear network mixing coefficients for code constructions of general connections that generalize random linear network coding (RLNC) for multicast connections. For such code constructions, we pose the problem of cost minimization for the subgraph involved in the coding solution and relate this minimization to a Constraint Satisfaction Problem (CSP) which we show can be simplified to have a moderate number of constraints. While CSPs are NP-complete in general, we present a probabilistic distributed algorithm with almost sure convergence in finite time by applying Communication Free Learning (CFL). Our approach allows fairly general coding across flows, guarantees no greater cost than routing, and shows a possible distributed implementation
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