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

• Published in: IEEE transactions on information theory Vol. 60; no. 12; pp. 7547 - 7567
• Main Authors: Song, Lin, Shao, Shuo, Chen, Jun
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Codes; Computers; Decoding; Distortion measurement; Encoding; Erasure distortion; Hamming distortion; Information theory; Markov processes; mean squared error; minimax theorem; multiple description coding; Normal distribution; saddle point; Theorems; Tin; Zinc; minimax theorem; multiple description coding; saddle point; mean squared error; Erasure distortion; Hamming distortion
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2014.2360698

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.