On feedback in network source coding

We consider source coding over networks with unlimited feedback from the sinks to the sources. We first show examples of networks where the rate region with feedback is a strict superset of that without feedback. Next, we find an achievable region for multiterminal lossy source coding with feedback. Finally, we evaluate this region for the case when one of the sources is fully known at the decoder and use the result to show that this region is a strict superset of the best known achievable region for the problem without feedback

On Zero-Error Source Coding with Feedback

We consider the problem of zero error source coding with limited feedback when side information is present at the receiver. First, we derive an achievable rate region for arbitrary joint distributions on the source and the side information. When all source pairs of source and side information symbols are observable with non-zero probability, we show that this characterization gives the entire rate region. Next, we demonstrate a class of sources for which asymptotically zero feedback suffices to achieve zero-error coding at the rate promised by the Slepian-Wolf bound for asymptotically lossless coding. Finally, we illustrate these results with the aid of three simple examples

On achievable rates for multicast in the presence of side information

We investigate the network source coding rate region for networks with multiple sources and multicast demands in the presence of side information, generalizing earlier results on multicast rate regions without side information. When side information is present only at the terminal nodes, we show that the rate region is precisely characterized by the cut-set bounds and that random linear coding suffices to achieve the optimal performance. When side information is present at a non-terminal node, we present an achievable region. Finally, we apply these results to obtain an inner bound on the rate region for networks with general source-demand structures

Concatenated Polar Codes

Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that for current constructions the probability of error decays sub-exponentially in the block-length (more detailed designs improve the probability of error at the cost of significantly increased computational complexity \cite{KorUS09}). In this work we show how the the classical idea of code concatenation -- using "short" polar codes as inner codes and a "high-rate" Reed-Solomon code as the outer code -- results in substantially improved performance. In particular, code concatenation with a careful choice of parameters boosts the rate of decay of the probability of error to almost exponential in the block-length with essentially no loss in computational complexity. We demonstrate such performance improvements for three sets of information-theoretic problems -- a classical point-to-point channel coding problem, a class of multiple-input multiple output channel coding problems, and some network source coding problems

A Continuity Theory for Lossless Source Coding over Networks

A continuity theory of lossless source coding over networks is established and its implications are investigated. In the given model, source and side-information random variables X and Y have finite alphabets, and the input sequences are drawn i.i.d. according to a generic distribution P_(X,Y) on (X,Y). We consider traditional source coding, where all demands equal source random variables. We define a family of lossless source coding problems that includes prior example network source coding problems as special cases. We show that the lossless rate region R_L(P_(X,Y)) is inner semi-continuous in P_(X,Y). We further show that for a special type of networks called super-source networks, where there is a super source node v* that has access to (X,Y) and any other node with access to some source random variable X_i is directly connected to v*, R_L(P_(X,Y)) is also outer semi-continuous in P_(X,Y). Based on the continuity of super-source networks with respect to P_(X,Y), we conjecture that R_L(P_(X,Y)) is also outer semi-continuous and therefore continuous in P_(X,Y) for general networks

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