A Lower Bound on the Sum Rate of Multiple Description Coding With Symmetric Distortion Constraints

We derive a single-letter lower bound on the minimum sum rate of multiple description coding with symmetric distortion constraints. For the binary uniform source with the erasure distortion measure or Hamming distortion measure, this lower bound can be evaluated with the aid of certain minimax theorems. A similar minimax theorem is established in the quadratic Gaussian setting, which is further leveraged to analyze the special case where the minimum sum rate subject to two levels of distortion constraints (with the second level imposed on the complete set of descriptions) is attained; in particular, we determine the minimum achievable distortions at the intermediate levels.