Multiple description coding over correlated multipath erasure channels

The problem of optimal rate allocation to streams constituting multiple description coding (MDC) has largely been addressed under the assumption that the multiple paths available for transmission are uncorrelated. In this paper, we model the transmission paths as correlated erasure channels and then examine the problem of allocating a given coding rate to the multiple descriptions in order to minimize the average distortion of the reconstructed message. We also investigate the relationship between the optimal average distortion and correlation of channels and prove that the bound on the average distortion will decrease as the correlation increases. Furthermore, we derive a closed-form solution for the contour which determines the region where multiple description coding (MDC) or single description coding (SDC) yields the minimal bound on the average distortion. Relying on this contour, we present a heuristic of the optimal rate allocation problem to determine the number of descriptions and relative rates.