1,436 research outputs found
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
Protection against link errors and failures using network coding
We propose a network-coding based scheme to protect multiple bidirectional
unicast connections against adversarial errors and failures in a network. The
network consists of a set of bidirectional primary path connections that carry
the uncoded traffic. The end nodes of the bidirectional connections are
connected by a set of shared protection paths that provide the redundancy
required for protection. Such protection strategies are employed in the domain
of optical networks for recovery from failures. In this work we consider the
problem of simultaneous protection against adversarial errors and failures.
Suppose that n_e paths are corrupted by the omniscient adversary. Under our
proposed protocol, the errors can be corrected at all the end nodes with 4n_e
protection paths. More generally, if there are n_e adversarial errors and n_f
failures, 4n_e + 2n_f protection paths are sufficient. The number of protection
paths only depends on the number of errors and failures being protected against
and is independent of the number of unicast connections.Comment: The first version of this paper was accepted by IEEE Intl' Symp. on
Info. Theo. 2009. The second version of this paper is submitted to IEEE
Transactions on Communications (under minor revision). The third version of
this paper has been accepted by IEEE Transactions on Communication
Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space
In asymptotic regimes, both in time and space (network size), the derivation
of network capacity results is grossly simplified by brushing aside queueing
behavior in non-Jackson networks. This simplifying double-limit model, however,
lends itself to conservative numerical results in finite regimes. To properly
account for queueing behavior beyond a simple calculus based on average rates,
we advocate a system theoretic methodology for the capacity problem in finite
time and space regimes. This methodology also accounts for spatial correlations
arising in networks with CSMA/CA scheduling and it delivers rigorous
closed-form capacity results in terms of probability distributions. Unlike
numerous existing asymptotic results, subject to anecdotal practical concerns,
our transient one can be used in practical settings: for example, to compute
the time scales at which multi-hop routing is more advantageous than single-hop
routing
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
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