Rainbow Network Flow with Network Coding

Rainbow network flow is a recent enquiry into rate-distortion optimized network flow of a multiple description (MD) coded source from multiple encoders to multiple sinks. This paper is a first attempt to combine network coding with rainbow network flow, and formulates a new problem called rainbow network coding (RNC). It is shown that performing linear network coding at intermediate nodes of a flow path can achieve higher network throughput than the original rainbow network flow solution. RNC is related to the linear broadcast problem defined in network coding theory, but it has a different objective function that is more meaningful for lossy signal compression applications than linear broadcast. We prove the RNC problem to be NP-hard, and propose some heuristic solutions. Examples are presented to study the differences between rainbow network coding, rainbow network flow, and linear broadcast.