Reliability criteria in information theory and in statistical hypothesis testing
Foundations and Trends in Communications and Information Theory
New results on multiple descriptions in the Wyner-Ziv setting
IEEE Transactions on Information Theory
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Multiple description source coding concerns situations in which the transmission of the source information is distributed over two data streams at rates R1 and R2, respectively. When both data streams are received, the decoder uses the combined data at rate R1+R2 to reconstruct the source information with average distortion d0. If a communication breakdown prevents one of the data streams from reaching the receiver, the decoder has to base its reconstruction solely on the available data at rate either R1 or R2. This results in a higher distortion of either d1 or d2, respectively. The region ℛ of all achievable quintuples (R1, R2, d0, d1, d2) has been determined in the so-called “no excess rate” sum case defined by imposing the requirement R1+R2=R(d0), where R(·) is the rate-distortion function of the source. The case with excess rate sum, characterized by R1+R2>R(d0), is challenging. We study in this paper a special case of it in which the requirements Rt=R(dt), t=1, 2, are imposed; we refer to this as the “no excess marginal rate” case. The lower and upper bounds on d0 we obtain are separated by only a tiny gap when evaluated for a binary equiprobable source and the Hamming distortion measure