On the Continuity of Achievable Rate Regions for Source Coding over Networks

The continuity property of achievable rate regions for source coding over networks is considered. We show rate- distortion regions are continuous with respect to distortion vectors. Then we focus on the continuity of lossless rate regions with respect to source distribution: First, the proof of continuity for general networks with independent sources is given; then, for the case of dependent sources, continuity is proven both in examples where one-letter characterizations are known and in examples where one-letter characterizations are not known; the proofs in the latter case rely on the concavity of the rate regions for those networks

Active Topology Inference using Network Coding

Our goal is to infer the topology of a network when (i) we can send probes between sources and receivers at the edge of the network and (ii) intermediate nodes can perform simple network coding operations, i.e., additions. Our key intuition is that network coding introduces topology-dependent correlation in the observations at the receivers, which can be exploited to infer the topology. For undirected tree topologies, we design hierarchical clustering algorithms, building on our prior work. For directed acyclic graphs (DAGs), first we decompose the topology into a number of two-source, two-receiver (2-by-2) subnetwork components and then we merge these components to reconstruct the topology. Our approach for DAGs builds on prior work on tomography, and improves upon it by employing network coding to accurately distinguish among all different 2-by-2 components. We evaluate our algorithms through simulation of a number of realistic topologies and compare them to active tomographic techniques without network coding. We also make connections between our approach and alternatives, including passive inference, traceroute, and packet marking

Lossless Source Coding in the Point-to-Point, Multiple Access, and Random Access Scenarios

This paper treats point-to-point, multiple access and random access lossless source coding in the finite-blocklength regime. A random coding technique is developed, and its power in analyzing the third-order coding performance is demonstrated in all three scenarios. Via a connection to composite hypothesis testing, a new converse that tightens previously known converses for Slepian-Wolf source coding is established. Asymptotic results include a third-order characterization of the Slepian-Wolf rate region and a proof showing that for dependent sources, the independent encoders used by Slepian-Wolf codes can achieve the same third-order-optimal performance as a single joint encoder. The concept of random access source coding, which generalizes the multiple access scenario to allow for a subset of participating encoders that is unknown a priori to both the encoders and the decoder, is introduced. Contributions include a new definition of the probabilistic model for a random access source, a general random access source coding scheme that employs a rateless code with sporadic feedback, and an analysis demonstrating via a random coding argument that there exists a deterministic code of the proposed structure that simultaneously achieves the third-order-optimal performance of Slepian-Wolf codes for all possible subsets of encoders.Comment: 42 pages, 10 figures. Part of this work was presented at ISIT'1

On Network Coding of Independent and Dependent Sources in Line Networks

We investigate the network coding capacity for line networks. For independent sources and a special class of dependent sources, we fully characterize the capacity region of line networks for all possible demand structures (e.g., multiple unicast, mixtures of unicasts and multicasts, etc.) Our achievability bound is derived by first decomposing a line network into single-demand components and then adding the component rate regions to get rates for the parent network. For general dependent sources, we give an achievability result and provide examples where the result is and is not tight