On the Separation of Lossy Source-Network Coding and Channel Coding in Wireline Networks

This paper proves the separation between source-network coding and channel coding in networks of noisy, discrete, memoryless channels. We show that the set of achievable distortion matrices in delivering a family of dependent sources across such a network equals the set of achievable distortion matrices for delivering the same sources across a distinct network which is built by replacing each channel by a noiseless, point-to-point bit-pipe of the corresponding capacity. Thus a code that applies source-network coding across links that are made almost lossless through the application of independent channel coding across each link asymptotically achieves the optimal performance across the network as a whole.Comment: 5 pages, to appear in the proceedings of 2010 IEEE International Symposium on Information Theory (ISIT

Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks

A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver nodes. Source nodes transmit subspace projections of random correlated signals by applying reduced-dimension linear transforms. The subspace projections are linearly processed by multiple relays and routed to intended receivers. Each receiver applies a linear estimator to approximate a subset of the sources with minimum mean squared error (MSE) distortion. The model is extended to include noisy networks with power constraints on transmitters. A key task is to compute all local compression matrices and linear estimators in the network to minimize end-to-end distortion. The non-convex problem is solved iteratively within an optimization framework using constrained quadratic programs (QPs). The proposed algorithm recovers as special cases the regular and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the distortion region of multi-source, multi-receiver networks are given for linear coding based on convex relaxations. Cut-set lower bounds are also given for any coding strategy based on information theory. The distortion region and compression-estimation tradeoffs are illustrated for different communication demands (e.g. multiple unicast), and graph structures.Comment: 33 pages, 7 figures, To appear in IEEE Transactions on Signal Processin

Separation of Source-Network Coding and Channel Coding in Wireline Networks

In this paper, we prove the separation of source-network coding and channel coding in wireline networks. For the purposes of this paper, a wireline network is any network of independent, memoryless, point-to-point, and finite-alphabet channels used to transmit dependent sources either losslessly or subject to a distortion constraint. In deriving this result, we also prove that in a general memoryless network with dependent sources, lossless, and zero-distortion reconstruction are equivalent provided that the conditional entropy of each source given the other sources is nonzero. Furthermore, we extend the separation result to the case of continuous-alphabet and point-to-point channels, such as additive white Gaussian noise channels