Multiple Description Coding over Erasure Channels

In this paper, we study the optimal rate allocation of multiple description coding over multiple erasure channels in order to attain the minimum average distortion of the recovered message at the receiver. The results of this investigation are subsequently used to determine conditions under which the optimal rate allocation is characterized by transmission of one description over a single channel, i.e. single description coding. We formulate the optimal rate allocation problem by using rate- distortion theory under the constraint that the total coding rate is fixed and solve the problem by using numerical methods. Furthermore, we derive a closed-form analytical solution to the optimal rate allocation problem under four conditions and verify that the analytical solution is consistent with the numerical results. Also, we present a heuristic that captures the solution to the optimal rate allocation problem and can be used to determine the number of descriptions and relative rates required to achieve optimality.