Vector quantization and signal compression
Vector quantization and signal compression
Foundations of Quantization for Probability Distributions
Foundations of Quantization for Probability Distributions
Fixed-rate successively refinable scalar quantizers
DCC '96 Proceedings of the Conference on Data Compression
Entropy-Constrained Successively Refinable Scaler Quantization
DCC '97 Proceedings of the Conference on Data Compression
Quantization as Histogram Segmentation: Globally Optimal Scalar Quantizer Design in Network Systems
DCC '02 Proceedings of the Data Compression Conference
Codecell Contiguity in Optimal Fixed-Rate and Entropy-Constrained Network Scalar Quantizers
DCC '02 Proceedings of the Data Compression Conference
Algorithms for optimal multi-resolution quantization
Journal of Algorithms
Asymptotic analysis of multiple description quantizers
IEEE Transactions on Information Theory
On the structure of optimal entropy-constrained scalar quantizers
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Multiresolution vector quantization
IEEE Transactions on Information Theory
Lagrangian Optimization of Two-Description Scalar Quantizers
IEEE Transactions on Information Theory
Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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It is known that the generalized Lloyd method is applicable to locally optimal multiple description scalar quantizer (MDSQ) design. However, it remains unsettled when the resulting MDSQ is also globally optimal. We partially answer the above question by proving that for a fixed index assignment there is a unique locally optimal fixed-rate MDSQ of convex cells under Trushkin's sufficient conditions for the uniqueness of locally optimal fixed-rate single description scalar quantizer. This result holds for fixed-rate multiresolution scalar quantizer (MRSQ) of convex cells as well. Thus, the well-known log-concave probability density function (pdf) condition can be extended to the multiple description and multiresolution cases. Moreover, we solve the difficult problem of optimal index assignment for fixed-rate MRSQ and symmetric MDSQ, when cell convexity is assumed. In both cases we prove that at optimality the number of cells in the central partition has to be maximal, as allowed by the side quantizer rates. As long as this condition is satisfied, any index assignment is optimal for MRSQ, while for symmetric MDSQ an optimal index assignment is proposed. The condition of convex cells is also discussed. It is proved that cell convexity is asymptotically optimal for high resolution MRSQ, under the rth power distortion measure.