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This paper introduces an efficient polynomial-time code construction algorithm for cyclic networks, which achieves the optimal multicast rate. Until this work, no explicit capacity-achieving polynomial-time code construction for <i>cyclic</i> networks has been known. This new construction algorithm has the additional advantage that as sinks are added or(More)
— We present a new approach to network coding problems that could lead to a systematic method for deciding solvability of a given network. The approach is based on a graph theoretic formulation of the problem. The constraints at each node in the network are represented using hyperedges in a 'conflict' hypergraph. This representation reduces the solvability(More)
The capacity of multiuser networks has been a long-standing problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate wireless networks. For multicast, they have shown that the capacity for the deterministic model is equal to the minimal rank of the incidence matrix of a certain cut between the(More)
The capacity of multiuser networks has been a long-standing problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate multiuser wireless networks. This model, known as the ADT network model, takes into account the broadcast nature as well as the multiuser interference inherent in the wireless(More)
—In this paper we derive capacity regions for network error correction with both known and unknown topologies (coherent and non-coherent network coding) under a multiple-source multicast transmission scenario. For the multiple-source non-multicast scenario, given any achievable network code for the error-free case, we construct a code with a reduced rate(More)
We consider the problem of correcting errors and erasures with network coding. Unlike existing works which consider performance limits for worst-case locations of given numbers of errors and erasures, we consider the performance of given (not necessarily optimal) coding and forwarding strategies for given (not necessarily worst-case) models of error and(More)