7,416 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
Linear Network Coding for Two-Unicast- Networks: A Commutative Algebraic Perspective and Fundamental Limits
We consider a two-unicast- network over a directed acyclic graph of unit
capacitated edges; the two-unicast- network is a special case of two-unicast
networks where one of the destinations has apriori side information of the
unwanted (interfering) message. In this paper, we settle open questions on the
limits of network coding for two-unicast- networks by showing that the
generalized network sharing bound is not tight, vector linear codes outperform
scalar linear codes, and non-linear codes outperform linear codes in general.
We also develop a commutative algebraic approach to deriving linear network
coding achievability results, and demonstrate our approach by providing an
alternate proof to the previous results of C. Wang et. al., I. Wang et. al. and
Shenvi et. al. regarding feasibility of rate in the network.Comment: A short version of this paper is published in the Proceedings of The
IEEE International Symposium on Information Theory (ISIT), June 201
A Generalized Cut-Set Bound for Deterministic Multi-Flow Networks and its Applications
We present a new outer bound for the sum capacity of general multi-unicast
deterministic networks. Intuitively, this bound can be understood as applying
the cut-set bound to concatenated copies of the original network with a special
restriction on the allowed transmit signal distributions. We first study
applications to finite-field networks, where we obtain a general outer-bound
expression in terms of ranks of the transfer matrices. We then show that, even
though our outer bound is for deterministic networks, a recent result relating
the capacity of AWGN KxKxK networks and the capacity of a deterministic
counterpart allows us to establish an outer bound to the DoF of KxKxK wireless
networks with general connectivity. This bound is tight in the case of the
"adjacent-cell interference" topology, and yields graph-theoretic necessary and
sufficient conditions for K DoF to be achievable in general topologies.Comment: A shorter version of this paper will appear in the Proceedings of
ISIT 201
Capacity of wireless erasure networks
In this paper, a special class of wireless networks, called wireless erasure networks, is considered. In these networks, each node is connected to a set of nodes by possibly correlated erasure channels. The network model incorporates the broadcast nature of the wireless environment by requiring each node to send the same signal on all outgoing channels. However, we assume there is no interference in reception. Such models are therefore appropriate for wireless networks where all information transmission is packetized and where some mechanism for interference avoidance is already built in. This paper looks at multicast problems over these networks. The capacity under the assumption that erasure locations on all the links of the network are provided to the destinations is obtained. It turns out that the capacity region has a nice max-flow min-cut interpretation. The definition of cut-capacity in these networks incorporates the broadcast property of the wireless medium. It is further shown that linear coding at nodes in the network suffices to achieve the capacity region. Finally, the performance of different coding schemes in these networks when no side information is available to the destinations is analyzed
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