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We take a new look at the issue of network capacity. It is shown that network coding is an essential ingredient in achieving the capacity of a network. Building on recent work by Li <i>et al.</i>, who examined the network capacity of multicast networks, we extend the network coding framework to arbitrary networks and robust networking. For networks which(More)
We present a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks. Network nodes independently and randomly select linear mappings from inputs onto output links over some field. We show that this achieves capacity with probability exponentially approaching 1 with the code(More)
The problem of error-control in random linear network coding is considered. A ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that linear network coding is vector-space preserving, information(More)
We study the turbo equalization approach to coded data transmission over channels with intersymbol interference. In the original system invented by Douillard et al., the data are protected by a convolutional code and the receiver consists of two trellis-based detectors, one for the channel (the equalizer) and one for the code (the decoder). It has been(More)
A number of important advances have been made in the area of joint equalization and decoding of data transmitted over intersymbol interference (ISI) channels. Turbo equalization is an iterative approach to this problem, in which a maximum a posteriori probability (MAP) equalizer and a MAP decoder exchange soft information in the form of prior probabilities(More)
The problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of Rotter and Kschischang. A large class of constant-dimension subspace codes is investigated. It is shown that codes in this class can be easily constructed from rank-metric codes, while preserving their(More)
A polynomial-time soft-decision decoding algorithm for Reed–Solomon codes is developed. This list-decoding algorithm is algebraic in nature and builds upon the interpolation procedure proposed by Guruswami and Sudan for hard-decision decoding. Algebraic soft-decision decoding is achieved by means of converting the probabilistic reliability information into(More)
The goal of the present paper is the derivation of a framework for the finite-length analysis of message-passing iterative decoding of low-density parity-check codes. To this end we introduce the concept of graph-cover decoding. Whereas in maximum-likelihood decoding all codewords in a code are competing to be the best explanation of the received vector,(More)