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ABSTRACT: We consider the problem of characterizing network capacity in the presence of adversarial errors on network links, focusing in particular on the effect of low-capacity feedback links across network cuts. We give a new outer bound as well as a new achievable strategy, and show a family of networks where the inner and outer bounds coincide.
Information Theory and Applications Workshop (ITA), 2011; 03/2011
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ABSTRACT: ¿If we know more, we can achieve more.¿ This adage also applies to networks, where more information about the network state translates into higher sum-rates. In this paper, we formalize this increase of sum-rate with increased knowledge of network. The knowledge of network is measured in terms of the number of hops of information about the network while the sum-rate is normalized by the maximum sum-rate that can be achieved with complete information. As the knowledge about the network increase, the achievable normalized sum-rate also increases. The best normalized sum-rate is called normalized sum-capacity. In this paper, we characterize the increase of normalized sum-capacity with the hops of information about the network for many classes of deterministic interference networks for the cases of one and two-hops of instantaneous channel information.
Information Sciences and Systems (CISS), 2010 44th Annual Conference on; 04/2010
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ABSTRACT: In this paper, we present new results on network error correction with unequal link capacities. We consider network error correction codes that can correct arbitrary errors occurring on up to z links. We find the capacity of a two-node network with multiple feedback links and show how feedback links can be used to increase the error correction capacity. We propose a new cut-set upper bound for general acyclic networks, and show its tightness for a family of four-node acyclic networks when each backward link has enough capacity. For a more general family of zig-zag networks, we present conditions under which our upper bound is tight. Finally, we propose an approach for high-probability network error correction with a causal adversary.
Information Theory and Applications Workshop (ITA), 2010; 03/2010
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ABSTRACT: In distributed wireless networks, nodes often do not know the topology (network size, connectivity and the channel gains) of the network. Thus, they have to compute their transmission and reception parameters in a distributed fashion. In this paper, we consider the information required at the nodes to achieve globally optimal sum capacity. Our first result relates to the case when each of the transmitter know the channel gains of all the links that are at-most two-hop distant from it and the receiver knows the channel gains of all the links that are three-hop distant from it in a deterministic interference channel. With this limited information, we find that distributed decisions are sum-rate optimal only if each connected component is in a one-to-many configuration or a fully-connected configuration. In all other cases of network connectivity, the loss can be arbitrarily large. We then extend the result to see that O(K) hops of information are needed in general to achieve globally optimal solutions. To show this we consider a class of symmetric interference channel chain and find that in certain cases of channel gains, the knowledge of a particular user being odd user or even user is important thus needing O(K) hops of information at the nodes.
Signals, Systems and Computers, 2009 Conference Record of the Forty-Third Asilomar Conference on; 12/2009
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ABSTRACT: In this work, we address the following question: ¿When can we guarantee the optimality of linear coding at all internal nodes of a network?¿ While sufficient conditions for linear coding throughout the network are known, it is not clear whether relaxing the linearity constraints at the terminal nodes can result in simpler operations at the internal nodes. We present a novel method to analyze the space of network solutions using the constraints resulting from the network topology, and we identify sufficient conditions for an optimal linear solution at all internal nodes. These conditions are also sufficient to characterize the rate region only in terms of Shannon information inequalities.
Information Theory Workshop, 2009. ITW 2009. IEEE; 11/2009
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ABSTRACT: In distributed wireless networks, nodes often do not know the topology (network size, connectivity and the channel gains) of the network. Thus, they have to compute their transmission and reception parameters in a distributed fashion. In this paper, we consider that each of the transmitter know the channel gains of all the links that are at-most two-hop distant from it and the receiver knows the channel gains of all the links that are three-hop distant from it in a deterministic interference channel. With this limited information, we find a condition on the network connectivity for which there exist a distributed strategy that can be chosen by the users with partial information about the network state, which achieves the same sum capacity as that achievable by the centralized server that knows all the channel gains. Specifically, distributed decisions are sum-rate optimal only if each connected component is in a one-to-many configuration or a fully-connected configuration. In all other cases of network connectivity, the loss can be arbitrarily large.
Communication, Control, and Computing, 2009. Allerton 2009. 47th Annual Allerton Conference on; 11/2009
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ABSTRACT: We study network error correction with unequal link capacities. Previous results on network error correction assume unit link capacities. We consider network error correction codes that can correct arbitrary errors occurring on up to z links. We find the capacity of a network consisting of parallel links, and a generalized Singleton outer bound for any arbitrary network. We show by example that linear coding is insufficient for achieving capacity in general. In our example, the capacity is 50% greater than the linear coding capacity and we achieve using a nonlinear error detection strategy. We also present a method for finding an upper bound on the linear coding capacity for arbitrary network. We show that even for a single source and single sink network, it may be necessary for intermediate nodes to do coding, nonlinear error detection or error correction. This is unlike the equal link capacity case, where coding only at the source and forwarding at intermediate nodes suffices for a single source and sink network. We conjecture that the generalized Singleton outer bound is not achievable in general.
Communication, Control, and Computing, 2009. Allerton 2009. 47th Annual Allerton Conference on; 11/2009
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ABSTRACT: In this paper, we generalize the lossless coded side information problem from the three-node network of Ahlswede and Korner to more general network scenarios. We derive inner and outer bounds on the achievable rate region in the general network scenario and show that they are tight for some families of networks. Our approach demonstrates how solutions to canonical source coding problems can be used to derive bounds for more complex networks and reveals an interesting connection between networks with side information, successive refinement, and network coding.
Information Theory, 2009. ISIT 2009. IEEE International Symposium on; 08/2009
