  This work considers the problem of transmitting multiple compressible sources
over a network at minimum cost. The aim is to find the optimal rates at which
the sources should be compressed and the network flows using which they should
be transmitted so that the cost of the transmission is minimal. We consider
networks with capacity constraints and linear cost functions. The problem is
complicated by the fact that the description of the feasible rate region of
distributed source coding problems typically has a number of constraints that
is exponential in the number of sources. This renders general purpose solvers
inefficient. We present a framework in which these problems can be solved
efficiently by exploiting the structure of the feasible rate regions coupled
with dual decomposition and optimization techniques such as the subgradient
method and the proximal bundle method.
