Abstract
This chapter discusses the problem of communicating statistically dependent sources over networks, focusing in particular on the case of lossless reconstruction over acyclic networks of noise-free links. In contrast to a purely network coding setup with independent sources, optimal code design for this setup involves both network coding as well as data compression aspects. Calculating the set of achievable rates for this problem is a difficult task in general, though some continuity properties of the rate region are known, and a general outer bound can be obtained from cut-set arguments. Even though the cut-set bounds are not achievable for all networks, they are achievable for multicast networks, i.e., networks where all sources are demanded at all sinks. The cut-set bounds are also achievable for an extension of the multicast network, where, in addition to the desired sources, the network may have side information present at some of the sinks. For both these cases, cut-set bounds are achievable via linear network codes. Finally, some practical approaches to combining network coding and compression are discussed.
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