S.D. Servetto, V.A. Vaishampayan, and N.J.A. Sloane. "Multiple Description Lattice Vector Quantization". In Proc. Data Compression Conf. (DCC), Snowbird, UT, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....0 ratios starting from 6dB (staggered quantizers) An asymptotic analysis in high resolution conditions for this scheme was performed in [20] and, more importantly, the results were compared to the optimal solution of Ozarow. Many variations on this scheme were proposed in recent years; see, e.g. [16, 2, 21]. A special case of the MD problem, where d 1 (or d 2 ) is set to the maximum, is successive refinement (SR) 5] This problem has a complete information theoretic solution as well as practical ones. A sub optimum method for multiple descriptions based on SR was suggested in [27] Roughly, using ....

.... average entropy of the side error, where M denotes the number of central cells composing a side cell (it is 2m 1 in the scalar case) Applying the same derivation with these substitutions, we get 2R Gamma TR o = 1 2 GKG side D(X;X ) log(2 ) It follows from the derivation in [16] that there exists lattice based constructions with G side = G K , and for which the term log(2 ) above vanishes. Appendix A Proof of Lemma 1 We first prove an auxiliary Lemma: Lemma 2. The joint density function of (X; X N 1 ; X N 2 ) is equal to the joint density function of (X; Q ....

S. Servetto, V. Vaishampayan, and N. Sloane, Multiple description lattice vector quantization, Proc. Data Compression Conference, Snowbird, March 1999, pp. 13--22.

....with a good single description quantizer using an index set and build an index assignment (IA) mapping from 2 , 1 and 2 are index sets for the side descriptions. This approach is used for scalar quantizer by Vaishampayan [96] for multiple description lattice vector quantizers in [90], 29] and tackled in a more abstract fashion by Berger Wolf and Reingold [11] 10] The IA function can be conveniently represented by an arrangement of the central indices in a matrix of size I . Each nonempty cell in the matrix defines a pair of side indices and contains the central ....

S. D. Servetto, V. A. Vaishampayan, and N. J. A. Sloane. Multiple description lattice vector quantization. In Proc. IEEE Data Compression Conf., 1999.

....considered the case of two descriptions. Theoretical results for the achievable rate region include results in [44, 79] Currently the achievable rate distortion is completely known only for the two channel memoryless Gaussian source. Recent work in the area of multiple descriptions includes [80, 81, 82, 83, 84, 85, 86, 87]. Previous work on MD coding includes methods which allow a wide range of redundancy levels to be introduced across a small set of descriptions (usually two descriptions) The MD scalar quantizer in [45] uses an index assignment to map a regular quantizer index to a pair of indices with a ....

....For the multidimensional multiple description coder, the challenge is improving the case where a large number of descriptions, moderate to low redundancy, and low quantizer resolution are simultaneously required for certain coefficients. Extensions from scalar to vector multiple descriptions as in [84] including complexity constraints would provide an additional challenge. The protection of watermarking information is another interesting research direction. Watermarking is used to identify intellectual property ownership. Ideally the watermarking 120 information should not noticeably distort ....

S. Servetto, V. Vaishampayan, and N. Sloane, "Multiple description lattice vector quantization, " Proceedings DCC '99. Data Compression Conference, 1999, pp. 13--22.

....address correspondence to Justin Ridge, e mail: jridge seas.smu.edu. result is achieved irrespective of which description(s) is received. In this paper, MDC refers to coders which adhere to the information theory meaning of multiple descriptions[4] including those presented in [5] 6] and [7], rather than those which, although appearing under the MDC banner, employ statistical channel models[8] The ability of multiple description coding to guarantee an absolute lower bound on quality, even under very lossy conditions, has led to its increasing popularity. However, in imposing such a ....

S. D. Servetto, V. A. Vaishampayan, and N. J. A. Sloane, "Multiple description lattice vector quantization," in Proc. Data Compression Conference, Snowbird, UT, March 1999.

.... while limiting the computational burden, we concentrate on multiple description lattice vector quantization (MDLVQ) instead of less constrained methods (see, e.g. 3] This paper begins, in Section 2, by reviewing the MDLVQ technique proposed last year by Servetto, Vaishampayan, and Sloane (SVS) [4]. The SVS algorithm is presented for squared error distortion, and we maintain that here. Section 3 provides variations on the SVS algorithm. We observe that the SVS encoder minimizes D 0 and propose instead a family of encoders that trade off D 0 and D 1 . Since MD techniques are only useful when ....

....is computationally expensive. Restricting codebooks to lattices simplifies the necessary calculations for encoding and decoding. The problem now becomes that of choosing a lattice and designing a way of assigning the indices. Servetto, Vaishampayan, and Sloane (SVS) provided such an algorithm in [4]. Since our algorithms build upon the original algorithm of SVS, it is summarized here for completeness. We will need the concept of a geometrically similar sublattice: Definition 1 Let be a lattice. 0 is a geometrically similar sublattice of if the points of 0 are a subset of the points ....

[Article contains additional citation context not shown here]

S. D. Servetto, V. A. Vaishampayan, and N. J. A. Sloane. Multiple description lattice vector quantization. In Proc. IEEE Data Compression Conf., pages 13--22, Snowbird, Utah, April 1999.

.... while limiting the computational burden, we concentrate on multiple description lattice vector quantization (MDLVQ) instead of less constrained methods (see, e.g. 3] This paper begins, in Section 2, by reviewing the MDLVQ technique proposed last year by Servetto, Vaishampayan, and Sloane (SVS) [4]. The SVS algorithm is presented for squared error distortion, and we maintain that here. Section 3 provides variations on the SVS algorithm. We observe that the SVS encoder minimizes D 0 and propose instead a family of encoders that trade o# D 0 and D 1 . Since MD techniques are only useful when ....

....is computationally expensive. Restricting codebooks to lattices simplifies the necessary calculations for encoding and decoding. The problem now becomes that of choosing a lattice and designing a way of assigning the indices. Servetto, Vaishampayan, and Sloane (SVS) provided such an algorithm in [4]. Since our algorithms build upon the original algorithm of SVS, it is summarized here for completeness. We will need the concept of a geometrically similar sublattice: Definition 1 Let # be a lattice. # # is a geometrically similar sublattice of # if the points of # # are a subset of the points ....

[Article contains additional citation context not shown here]

S. D. Servetto, V. A. Vaishampayan, and N. J. A. Sloane. Multiple description lattice vector quantization. In Proc. IEEE Data Compression Conf., pages 13--22, Snowbird, Utah, April 1999.

....assignment. In that formulation we start from a good single description quantizer using an index set I and build an index assignment mapping from I to I 1 I 2 , where I 1 and I 2 are index sets for the side descriptions. This approach is used for multiple description lattice vector quantizers in [8] and tackled in a more abstract fashion in [9] In this paper, we propose a tree structured approach for the implementation of the mapping . TSVQ provide good coding performance with linear complexity in the bitrate, instead of the exponential complexity of full search quantizers. This exible ....

S. D. Servetto, V. A. Vaishampayan, and N. J. A. Sloane. Multiple description lattice vector quantization. In Proc. IEEE Data Compression Conf., 1999.

....shown. I. Introduction Lattice vector quantization constrains a codebook to be a lattice (or large subset of a lattice) to dramatically reduce the complexity of nearest neighbor encoding. The multiple description lattice vector quantizers introduced by Servetto, Vaishampayan, and Sloane (SVS) [1] additionally use highly symmetric labelings of sublattice points to produce two descriptions corresponding to each codebook element. This correspondence describes the result of modifying the encoding and decoding to minimize a weighted combination of central and side distortions, while keeping ....

....in blocks of length K (K dimensional vector quantizers) that can be designed and implemented easily. Entropy coding of quantizer outputs is assumed, as is a moderate to high rate and squared error distortion. Under these assumptions, the MD lattice vector quantization (MDLVQ) technique of SVS [1] is a very attractive way to produce two descriptions. The encoder does a nearest neighbor search in a lattice # and then applies an index assignment mapping # to get an ordered pair of descriptions in a sublattice # # . The nearest neighbor search is simple because of the lattice structure, and ....

[Article contains additional citation context not shown here]

S. D. Servetto, V. A. Vaishampayan, and N. J. A. Sloane. Multiple description lattice vector quantization. In Proc. IEEE Data Compression Conf., pages 13--22, Snowbird, Utah, March 1999.

No context found.

S.D. Servetto, V.A. Vaishampayan, and N.J.A. Sloane. "Multiple Description Lattice Vector Quantization". In Proc. Data Compression Conf. (DCC), Snowbird, UT, 1998.

....Early papers on MD coding are information theoretic in nature, and deal with the problem of finding sets of achievable values for the quintuple (R 1 ; R 2 ; D 0 ; D 1 ; D 2 ) 3, 7] More recent papers however consider the problem of designing practical MD systems. MD quantizers are designed in [8, 10]. A suitable blockwise transform is applied to an input vector before coding to obtain the MD property in [4, 6] the input vector is usually a jointly Gaussian vector, the basic idea being to decorrelate the vector components and then to introduce again correlation between coefficients but in a ....

S.D. Servetto, V.A. Vaishampayan, and N.J.A. Sloane. "Multiple Description Lattice Vector Quantization". In Proc. Data Compression Conf. (DCC), Snowbird, UT, 1998.

.... multiple description quantizer design, including a formulation and solution of the underlying labeling problem in one dimension, was presented in [26] An asymptotic performance analysis of this quantizer was presented in [4] A preliminary version of the work presented here was first presented in [25]. Lattice quantizers (for the single description problem) have been extensively studied. In [31] a random quantization argument is used to give upper and lower bounds on the performance of quantizers for a fixed dimension. Detailed descriptions of the Voronoi regions of specific lattices are given ....

S. D. Servetto, V. A. Vaishampayan and N. J. A. Sloane, "Multiple description lattice vector quantization,", in Proceedings 1999 Data Compression Conference, pp. 13--22, IEEE Press, 1999.

.... for the more important descriptions to be available (as in successive refinement) For previous work on the information theoretic aspects of the multiple description problem see [2, 3, 4, 5, 6] The problem of designing quantizers for the multiple description problem has been considered in [7, 1, 8, 9, 10, 11]. The work presented here is for the asymmetric case, and extends the work in [9] which considered the balanced case. Unlike the work in [1] we do not use a training approach; instead we use the geometry of the underlying lattice to solve a labeling problem. Other approaches to multiple ....

.... work on the information theoretic aspects of the multiple description problem see [2, 3, 4, 5, 6] The problem of designing quantizers for the multiple description problem has been considered in [7, 1, 8, 9, 10, 11] The work presented here is for the asymmetric case, and extends the work in [9] which considered the balanced case. Unlike the work in [1] we do not use a training approach; instead we use the geometry of the underlying lattice to solve a labeling problem. Other approaches to multiple description coding based on overcomplete expansions are presented in [12, 13, 14] and ....

S. D. Servetto, V. A. Vaishampayan, and N. J. A. Sloane, "Multiple description lattice vector quantization," in Proceedings, Data Compression Conference, pp. 13--22, March 29-31 1999.

....s leads to fine quantization but poor ability to discriminate among codewords within each partition of , large s leads to good discrimination ability but coarse quantization. The question of the existence of similar sublattices arose recently in connection with another vector quantization problem [9], and also in the study of symmetries of 1 Two lattices 1 and 2 (with generator matrices M 1 and M 2 ) are said to be similar when there exist a constant c 6= 0, a matrix U with integer entries and jdet(U)j = 1, and a real matrix B with BB = I , such that M 2 = c UM 1 B [3] Intuitively, ....

S. D. Servetto, V. A. Vaishampayan, and N. J. A. Sloane. Multiple Description Lattice Vector Quantization. In Proc. IEEE Data Compression Conf. (DCC), Snowbird, UT, 1999.

....R 1 ds(R)2 2R(1 Gammaa) 2 2h(p) 2e : 2) Thus in multiple description quantization it is possible to achieve a reduction in the granular distortion by 1.53 dB, simultaneously for the two channel and the side distortion. The goal of this paper is to analyze constructions given in [3] for closing this 1.53 dB gap. The system to be analyzed is illustrated in Fig. 1. Our approach is as follows. From classical quantization theory, we know that the gap between scalar quantization and the rate distortion bound may channel 2 channel 1 Labeling Function Quantizer Lattice Source ....

S. D. Servetto, V. A. Vaishampayan and N. J. A. Sloane, "Multiple Description Lattice Vector Quantization", in Proceedings 1999 Data Compression Conference, pp. 13--22, IEEE Press, 1999.

.... for the more important descriptions to be available (as in successive refinement) For previous work on the information theoretic aspects of the multiple description problem see [2, 3, 4, 5, 6] The problem of designing quantizers for the multiple description problem has been considered in [7, 1, 8, 9, 10, 11]. The work presented here is for the asymmetric case, and extends the work in [9] which considered the balanced case. Unlike the work in [1] we do not use a training approach; instead we use the geometry of the underlying lattice to solve a labeling problem. Other approaches to multiple ....

.... work on the information theoretic aspects of the multiple description problem see [2, 3, 4, 5, 6] The problem of designing quantizers for the multiple description problem has been considered in [7, 1, 8, 9, 10, 11] The work presented here is for the asymmetric case, and extends the work in [9] which considered the balanced case. Unlike the work in [1] we do not use a training approach; instead we use the geometry of the underlying lattice to solve a labeling problem. Other approaches to multiple description coding based on overcomplete expansions are presented in [12, 13, 14] and ....

S. D. Servetto, V. A. Vaishampayan, and N. J. A. Sloane, "Multiple description lattice vector quantization," in Proceedings, Data Compression Conference, pp. 13--22, March 29-31 1999.

.... multiple description quantizer design, including a formulation and solution of the underlying labeling problem in one dimension, was presented in [22] An asymptotic performance analysis of this quantizer was presented in [3] A preliminary version of the work presented here was first presented in [21]. Lattice quantizers (for the single description problem) have been extensively studied. In [26] a random quantization argument is used to give upper and lower bounds on the performance of quantizers for a fixed dimension. Detailed descriptions of the Voronoi regions of specific lattices are given ....

S. D. Servetto, V. A. Vaishampayan and N. J. A. Sloane, "Multiple description lattice vector quantization," in Proceedings 1999 Data Compression Conference, pp. 13--22, IEEE Press, 1999.

....these two quantizers using the ideas of Trellis Coded Quantization (TCQ) 21] MD TCQ has been studied by a number of authors [2, 17, 37] and gains of up to 2:2dB over the performance of the MD scalar quantizer have been reported. MD Lattice Vector Quantization. Servetto, Vaishampayan and Sloane [30] give an explicit construction of the index assignments to be used in conjunction with vector quantizers based on a certain family of lattices endowed with a rich algebraic structure. 2.3 Subspace Projection Methods for the Generation of Multiple Descriptions This method was first proposed by ....

S. Servetto, V. Vaishampayan, and N. Sloane. Multiple-Description Lattice Vector Quantization. In Submitted to the IEEE Data Compression Conference, Snowbird, UT, 1999.

No context found.

Servetto S.D., Vaishampayan V.A. and Sloane N.J.A., Multiple Description Lattice Vector Quantization, in Proceedings of the IEEE Data Compression Conference, p. 1999.

No context found.

S.D. Servetto, V.A. Vaishampayan, and N.J.A. Sloane, "Multiple description lattice vector quantization," in Proc. IEEE Data Compression Conf., Snowbird, UT, Mar. 1999, pp. 13-22.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC