Rainbow Network Problems and Multiple Description Coding

In packet switched networks receivers can get packets of a multiple description code (MDC) from different sources for enhanced QoS and robust transmission. The quality achieved by a decoder increases in the number of distinct rather than the total number of packets received. This property makes the problems of optimizing network flows and transmission strategies for MDC, called rainbow network problems, very different from those of conventional network flow and management. Two interesting problems: rainbow network flow and rainbow multicast, are formulated and treated. The rainbow network flow problem of maximizing the number of distinct packets received, constrained by edge capacities, is shown to be NP-hard in multisource-multisink setting. But it can be reduced to conventional maximum network flow problem in the case of single sink, hence becomes solvable in polynomial time. Rainbow multicast problem is about coordinating multiple servers for minimum expected distortion at one or a set of clients. Although being seemingly intractable in general, some variants of the problem have analytical solutions.