  This paper considers the problem of minimum cost communication of correlated
sources over a network with multiple sinks, which consists of distributed
source coding followed by routing. We introduce a new routing paradigm called
dispersive information routing, wherein the intermediate nodes are allowed to
`split' a packet and forward subsets of the received bits on each of the
forward paths. This paradigm opens up a rich class of research problems which
focus on the interplay between encoding and routing in a network. Unlike
conventional routing methods such as in [1], dispersive information routing
ensures that each sink receives just the information needed to reconstruct the
sources it is required to reproduce. We demonstrate using simple examples that
our approach offers better asymptotic performance than conventional routing
techniques. This paradigm leads to a new information theoretic setup, which has
not been studied earlier. We propose a new coding scheme, using principles from
multiple descriptions encoding [2] and Han and Kobayashi decoding [3]. We show
that this coding scheme achieves the complete rate region for certain special
cases of the general setup and thereby achieves the minimum communication cost
under this routing paradigm.
