Optimal multichannel communication under failure
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Design of Asymmetric Multiple Description Lattice Vector Quantizers
DCC '00 Proceedings of the Conference on Data Compression
Successive Refinement on Trees: A Special Case of a New MD Coding Region
DCC '01 Proceedings of the Data Compression Conference
Reliability criteria in information theory and in statistical hypothesis testing
Foundations and Trends in Communications and Information Theory
Topics in Multi-User Information Theory
Foundations and Trends in Communications and Information Theory
Vector Gaussian multiple description with two levels of receivers
IEEE Transactions on Information Theory
New results on multiple descriptions in the Wyner-Ziv setting
IEEE Transactions on Information Theory
Multiple description coding for stationary Gaussian sources
IEEE Transactions on Information Theory
Approximating the Gaussian multiple description rate region under symmetric distortion constraints
IEEE Transactions on Information Theory
Consolidating achievable regions of multiple descriptions
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Multiple description coding of discrete ergodic sources
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
IEEE Transactions on Information Theory
Asymmetric multilevel diversity coding and asymmetric Gaussian multiple descriptions
IEEE Transactions on Information Theory
On multiple description coding of sources with memory
IEEE Transactions on Communications
New coding schemes for the symmetric K -description problem
IEEE Transactions on Information Theory
IEEE Transactions on Communications
Tabu search based multi-watermarks embedding algorithm with multiple description coding
Information Sciences: an International Journal
Suppressing the Cliff Effect in Video Reproduction Quality
Bell Labs Technical Journal
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An encoder whose input is a binary equiprobable memoryless source produces one output of rateR_{1}and another of rateR_{2}. LetD_{1}, D_{2}, and D_{0}, respectively, denote the average error frequencies with which the source data can be reproduced on the basis of the encoder output of rateR_{l}only, the encoder output of rateR_{2}only, and both encoder outputs. The two-descriptions problem is to determine the regionRof all quintuples(R_{1}, R_{2}, D_{1}, D_{2}, D_{0})that are achievable in thc usual Shannon sense. LetR(D)=1+D log_{2} D+(1-D) log_{2}(1-D)denote the error frequency rate-distortion function of the source. The "no excess rate case" prevails whenR_{1} + R_{2} = R(D_{0}), and the "excess rate case" whenR_{1} + R_{2} > R(D_{0}). Denote the section ofRat(R_{1}, R_{2}, D_{0})byD(R_{1} R_{2}, D_{0}) ={(D_{1},D_{2}): (R_{1}, R_{2}, D_{1},D_{2},D_{0}) in R}. In the no excess rate case we show that a portion of the boundary ofD(R_{1}, R_{2}, D_{0})coincides with the curve(frac{1}{2} + D_{1}-2D_{0})(frac_{1}_{2} + D_{2}-2D_{0})= frac{1}{2}(1-2D_{0})^{2}. This curve is an extension of Witsenhausen's hyperbola bound to the caseD_{0} > 0. It follows that the projection ofRonto the(D_{1}, D_{2})-plane at fixedD_{0}consists of allD_{1} geq D_{0}andD_{2} geq D_{0}that lie on or above this hyperbola. In the excess rate case we show by counterexample that the achievable region of El Gamal and Cover is not tight.