On the worst-case complexity of integer Gaussian elimination
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Singularity Probabilities for Random Matrices over Finite Fields
Combinatorics, Probability and Computing
Convex Optimization
Comprehensive view of a live network coding P2P system
Proceedings of the 6th ACM SIGCOMM conference on Internet measurement
Multimedia over IP and Wireless Networks: Compression, Networking, and Systems
Multimedia over IP and Wireless Networks: Compression, Networking, and Systems
On practical design for joint distributed source and network coding
IEEE Transactions on Information Theory
Joint source-channel coding for transmitting correlated sources over broadcast networks
IEEE Transactions on Information Theory
Network coding for distributed storage systems
IEEE Transactions on Information Theory
Handbook of Signal Processing Systems
Handbook of Signal Processing Systems
IEEE Transactions on Information Theory
Noiseless coding of correlated information sources
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Network information flow with correlated sources
IEEE Transactions on Information Theory
Separating distributed source coding from network coding
IEEE Transactions on Information Theory
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This paper considers a framework where data from correlated sources are transmitted with the help of network coding in ad hoc network topologies. The correlated data are encoded independently at sensors and network coding is employed in the intermediate nodes in order to improve the data delivery performance. In such settings, we focus on the problem of reconstructing the sources at decoder when perfect decoding is not possible due to losses or bandwidth variations. We show that the source data similarity can be used at decoder to permit decoding based on a novel and simple approximate decoding scheme. We analyze the influence of the network coding parameters and in particular the size of finite coding fields on the decoding performance. We further determine the optimal field size that maximizes the expected decoding performance as a trade-off between information loss incurred by limiting the resolution of the source data and the error probability in the reconstructed data. Moreover, we show that the performance of the approximate decoding improves when the accuracy of the source model increases even with simple approximate decoding techniques. We provide illustrative examples showing how the proposed algorithm can be deployed in sensor networks and distributed imaging applications.