Network Information Flow with Correlated Sources

In this paper, we consider a network communications problem in which multiple correlated sources must be delivered to a single data collector node, over a network of noisy independent point-to-point channels. We prove that perfect reconstruction of all the sources at the sink is possible if and only if, for all partitions of the network nodes into two subsets S and S^c such that the sink is always in S^c, we have that H(U_S|U_{S^c}) < \sum_{i\in S,j\in S^c} C_{ij}. Our main finding is that in this setup a general source/channel separation theorem holds, and that Shannon information behaves as a classical network flow, identical in nature to the flow of water in pipes. At first glance, it might seem surprising that separation holds in a fairly general network situation like the one we study. A closer look, however, reveals that the reason for this is that our model allows only for independent point-to-point channels between pairs of nodes, and not multiple-access and/or broadcast channels, for which separation is well known not to hold. This ``information as flow'' view provides an algorithmic interpretation for our results, among which perhaps the most important one is the optimality of implementing codes using a layered protocol stack.Comment: Final version, to appear in the IEEE Transactions on Information Theory -- contains (very) minor changes based on the last round of review

Non-Adaptive Distributed Compression in Networks

In this paper, we discuss non-adaptive distributed compression of inter-node correlated real-valued messages. To do so, we discuss the performance of conventional packet forwarding via routing, in terms of the total network load versus the resulting quality of service (distortion level). As a better alternative for packet forwarding, we briefly describe our previously proposed one-step Quantized Network Coding (QNC), and make motivating arguments on its advantage when the appropriate marginal rates for distributed source coding are not available at the encoder source nodes. We also derive analytic guarantees on the resulting distortion of our one-step QNC scenario. Finally, we conclude the paper by providing a mathematical comparison between the total network loads of one-step QNC and conventional packet forwarding, showing a significant reduction in the case of one-step QNC.Comment: Submitted for 2013 IEEE International Symposium on Information Theor

Linear Finite-Field Deterministic Networks With Many Sources and One Destination

We find the capacity region of linear finite-field deterministic networks with many sources and one destination. Nodes in the network are subject to interference and broadcast constraints, specified by the linear finite-field deterministic model. Each node can inject its own information as well as relay other nodes' information. We show that the capacity region coincides with the cut-set region. Also, for a specific case of correlated sources we provide necessary and sufficient conditions for the sources transmissibility. Given the "deterministic model" approximation for the corresponding Gaussian network model, our results may be relevant to wireless sensor networks where the sensing nodes multiplex the relayed data from the other nodes with their own data, and where the goal is to decode all data at a single "collector" node.Comment: 5 pages, 3 figures, submitted to ISIT 201