The networks studied in network source coding literature are typically directed, acyclic graphs. Just as it is well known that feedback cannot increase the capacity of the canonical point-to-point channel, it is also evident that feedback cannot increase the rate region of canonical point-to-point source coding problems. In this talk, we examine the role of feedback in network source coding.
Noting the limitations of usual information theoretic methods in networks with feedback, we approach this problem by making simplifying assumptions that enable us to combine techniques from both communication complexity theory and traditional source coding to develop insights into such systems.
First, we obtain the achievable rate region for multicast networks with one side information source assuming unbounded rate of feedback, thus demonstrating that feedback from sinks to sources has the potential to alter the rate region. Next, we derive inner and outer bounds on the achievable rate region under limited feedback. Finally, we explore the interactive nature of source coding in such systems by considering the problem of zero error source coding with side information. We present an achievable rate region for this problem which is tight under certain assumptions. We also show that in some cases, asymptotically zero rate of feedback is sufficient to achieve the Slepian-Wolf lower bound on the forward link.