V.A. Vaishampayan and J.-C. Batllo. Asymptotic analysis of multiple description quantizers. IEEE Trans. Information Theory, 44(1):278--284, January 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....distribution. This scheme is limited to the symmetric case (d 1 = d 2 ; R 1 = R 2 ) and to scalar quantization, and it covers only a discrete set of d 1 =d 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 ....

....correlation may explain the 1 2 bit loss in rate in the balanced description case. Furthermore the TSDQ suffers the space filling loss of three lattice quantizers. The work of Vaishampayan [19] on the multiple description scalar quantizer (MDSQ) seems promising in this sense. As shown in [20], it suffers the space filling loss of only two scalar quantizers at high resolution conditions. Furthermore, its side quantizer errors are negatively correlated as in Ozarow s test channel. We describe below a periodic dithered version of Vaishampayan s MDSQ, which incorporates linear ....

V. A. Vaishampayan and J.C. Batllo, Asymptotic analysis of multiple-description quantizers, IEEE Trans. Information Theory IT-44 (Jan. 1998), 278--284.

....tight. C. Code Constructions Several efforts have also been made to design practical MD coding systems. In [27] a design procedure for the construction of fixed rate scalar quantizers was presented. In [29] that design procedure was extended to the entropy constrained case. It is shown in [28] that at high rates, for the case of balanced descriptions (R 1 = R 2 = R) and Gaussian sources, the distortion product D 0 D 1 of the entropy constrained MD scalar quantizer takes the form: 4 ( At the same time, the MD rate distortion bound (when put in distortion product form) ....

V.A. Vaishampayan and J.-C. Batllo. Asymptotic analysis of multiple description quantizers. IEEE Trans. Information Theory, 44(1):278--284, January 1998.

....distortion product of MDSQ and the multiple description rate distortion bound is found to be 2.67 db for entropy constrained MDSQ (ECMDSQ) for any source with a smooth pdf, and 8.29 dB for level constrained MDSQ with a Gaussian source. These results are 0. 4 dB lower than previous results given in [1]. I. Introduction Multiple description coding achieves more graceful degradation in reconstruction performance than single description coding in the event of channel failure. Multiple description scalar quantization (MDSQ) 2] and entropyconstrained MDSQ (ECMDSQ) 3] achieve the multiple ....

....performance than single description coding in the event of channel failure. Multiple description scalar quantization (MDSQ) 2] and entropyconstrained MDSQ (ECMDSQ) 3] achieve the multiple description property in practical source coding systems. An asymptotic analysis for MDSQ ECMDSQ is given in [1]. In this paper, we introduce a new and straightforward asymptotic analysis of the multiple description scalar quantizer (MDSQ) The analysis provides insight into the structure of the MDSQ, suggesting the non optimality of uniform central quantizer cells in general. Using the mean squared error ....

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V.A. Vaishampayan and J.-C. Batllo, "Asymptotic analysis of multiple description quantizers," IEEE Trans. IT, vol. 44, no. 1, pp. 278--284, Jan 1998.

....is applied to optimizing two stage MDSQ in Section 5. Section 6 introduces the universal multiple description scalar quantizer and compares its performance with that of a traditionallydesigned ECMDSQ. 2 MDSQ and ECMDSQ The design and analysis of MDSQ and ECMDSQ were given in a series of papers [2, 1, 3] by Vaishampayan et al. We briefly review the results related to our work and then consider the implications of the asymptotic analysis. The basic idea of MDSQ is to create two coarse side quantizers which produce acceptable side distortions when used alone; the two coarse side quantizers are ....

....and an index assignment step. The system is depicted in Fig.1. Details about index assignment can be found in [2] Source a(l) p,q) Quantizer x q p Figure 1: Multiple description encoder diagram. To bound the asymptotic performance, the product of the central and side distortion is used [3] for Gaussian source with MSE measure. At high rates, if the side distortion is given by D 1 = b2 2(1 #)R (1) for some certain real number #,0# # 1, and R is the rate for one description, then the central distortion is given by D 0 # # # (b2 2R ) 2(b # b 1) # =0; 2 2R(1 #) 4b ....

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V.A. Vaishampayan and J.-C. Batllo, "Asymptotic analysis of multiple description quantizers," IEEE Trans. IT, vol. 44, no. 1, pp. 278--284, Jan 1998.

....MDSQ in [34] One of the most satising aspects of the theory of MDSQ is that at high rates, all the decay exponent trade offs discussed in Section II B can be obtained. Furthermore, the factor by which the distortion product DoDi exceeds the bounds of Theorem I is approximately constant [35]. For R R1 R2 and D1 D2, the bound for large rates is approximately DoD 4 while the performance of optimal fixed rate MDSQ is I 2 4 DoD eThere is no cenkral encoder, buk Q and Q2 effeckively implemenk a quankizer wikh cells given by khe inkerseckions of khe cells of khe individual ....

.... (UMDSQ s) described in detail in [29] The encoder for a UMDSQ operates as follows: A source sample is first uniformly quantized by rounding to the nearest multiple of a step size A; then, the index output by the scalar quantizer is mapped to a pair of indices using an index assignment based on [35]; finally, these indices are entropy coded. In all of the numerical results presented here, rate is measured by entropy rather than by the average code length of a particular code. Seven index assignments are used, giving seven operating points for each value of A; in the notation of [35] the ....

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V. A. Vaishampayan and J.-C. Batllo. Asymptotic analysis of multiple description quantizers. IEEE Trans. Inform. Th., 44(1):27884, January 1998.

....[573] In 1993 Vaishampayan et al. used a Lloyd algorithm to actually design fixed rate [508] and entropyconstrained [509] scalar quantizers for the multiple description problem. High resolution quantization ideas were used to evaluate achievable performance in 1998 by Vaishampayan and Batllo [510] and Linder, Zamir, and Zeger [324] An alternative approach to multiple description quantization using transform coding has also been considered, e.g. in [38] 211] I. Other Applications We have not treated many interesting variations and applications of quantization, several of which have ....

V. A. Vaishampayan and J.-C. Batllo "Asymptotic analysis of multiple description quantizers," IEEE Trans. Inform. Theory, vol. 44, pp. 278--284, Jan. 1998.

....[573] In 1993 Vaishampayan et al. used a Lloyd algorithm to actually design fixed rate [508] and entropyconstrained [509] scalar quantizers for the multiple description problem. High resolution quantization ideas were used to evaluate achievable performance in 1998 by Vaishampayan and Batllo [510] and Linder, Zamir, and Zeger [324] An alternative approach to multiple description quantization using transform coding has also been considered, e.g. in [38] 211] I. Other Applications We have not treated many interesting variations and applications of quantization, several of which have ....

V. A. Vaishampayan and J.-C. Batllo "Asymptotic analysis of multiple description quantizers," IEEE Trans. Inform. Theory, vol. 44, pp. 278--284, Jan. 1998.

....assume that d 1 = d 2 = d s and will refer to this common value as the side distortion. The objective is to design vector quantizers that minimize d 0 under the constraint d s D s , for a given rate pair (R; R) and a given bound D s on the side channel distortion. It has been shown [27] that for a uniform entropy coded multiple description quantizer, and any a 2 (0; 1) the distortions satisfy lim R 1 d 0 (R)2 2R(1 a) 1 4 2 2h(p) 12 ; lim R 1 d s (R)2 2R(1 Gammaa) 2 2h(p) 12 : 3) 1 INTRODUCTION 4 On the other hand, by using a random ....

V. Vaishampayan and J.-C. Batllo, "Asymptotic analysis of multiple description quantizers, " IEEE Trans. Inform. Th., vol. 44, pp. 278--284, Jan. 1998.

....quantization system for a discrete memoryless source with differential entropy h(p) The quantizer transmits information on each channel at rate R bits sample. The mean squared error when both channels work is denoted by d0 and when either channel works is denoted by ds . It has been shown [1] that for a uniform entropy coded multiple description quantizer and any a 2 (0; 1) the distortions satisfy lim R 1 d0(R)2 2R(1 a) 1 4 2 2h(p) 12 ; lim R 1 ds(R)2 2R(1 Gammaa) 2 2h(p) 12 : 1) On the other hand, by using a random quantizer argument it was shown ....

V. Vaishampayan and J.-C. Batllo, "Asymptotic analysis of multiple description quantizers," IEEE Trans. Inform. Th., vol. 44, pp. 278--284, Jan. 1998.

....the second description is available. We will further assume that d 1 = d 2 = d s and will refer to this common value as the side distortion. The objective is to design vector quantizers that minimize d 0 under the constraint d s # D s , for a given rate pair (R, R) It has been shown [23] that for a uniform entropy coded multiple description quantizer, and any a # (0, 1) the distortions satisfy lim R## d 0 (R)2 2R(1 a) 1 4 # 2 2h(p) 12 # , lim R## d s (R)2 2R(1 a) # 2 2h(p) 12 # . 3) On the other hand, by using a random quantizer argument it was ....

V. Vaishampayan and J.-C. Batllo, "Asymptotic analysis of multiple description quantizers, " IEEE Trans. Inform. Th., vol. 44, pp. 278--284, Jan. 1998.

....and Reingold [2] generalize the construction of index assignments from matrices for two channels to arbitrary k dimensional tensors for any number of channels. The exact coefficient of quantization (i.e. the sub exponential terms in the error expression) of the MD scalar quantizer was computed in [1], for general source densities and m th power distortion measures [6] Perhaps the most interesting case is that of a gaussian density and m = 2. Due to the large number of parameters involved (rates for each of the channels and distortions for all subsets of working nonworking channels) ....

....Perhaps the most interesting case is that of a gaussian density and m = 2. Due to the large number of parameters involved (rates for each of the channels and distortions for all subsets of working nonworking channels) comparisons between MD systems can get complicated. However, it is argued in [1] that in the balanced case (i.e. when the rates on the channels are equal) the product d 0 d 1 of the side and central distortions is a good figure of merit for high rates. For a gaussian source and m = 2, it was shown in [1] that there is a gap of 8.69dB between the distortion product of the ....

[Article contains additional citation context not shown here]

J.-C. Batllo and V. A. Vaishampayan. Asymptotic Analysis of Multiple Description Quantizers. IEEE Trans. Inform. Theory, 44(1):278--283, 1998.

....and Reingold [2] generalize the construction of index assignments from matrices for two channels to arbitrary k dimensional tensors for any number of channels. The exact coefficient of quantization (i.e. the sub exponential terms in the error expression) of the MD scalar quantizer was computed in [1], for general source densities and m th power distortion measures [8] Perhaps the most interesting case is that of a gaussian density and m = 2. Because of the large number of parameters involved (rates for each of the channels and distortions for all subsets of working nonworking channels) ....

....Perhaps the most interesting case is that of a gaussian density and m = 2. Because of the large number of parameters involved (rates for each of the channels and distortions for all subsets of working nonworking channels) comparisons between MD systems are complicated. However, it is argued in [1] that in the balanced case (i.e. when the rates on the channels are equal) the product d 0 d 1 of the side and central distortions is a good figure of merit for high rates. For a gaussian source and m = 2, it was shown in [1] that there is a gap of 8.69dB between the distortion product of the MD ....

[Article contains additional citation context not shown here]

J.-C. Batllo and V. A. Vaishampayan. Asymptotic Analysis of Multiple Description Quantizers. IEEE Trans. Inform. Theory, 44(1):278--283, 1998.

....of the MD scalar quantizer is bounded away from the gaussian MD rate distortion bound, as one would intuitively expect. that of the single description coder. The exact coefficient of quantization (i.e. the sub exponential terms in the error expression) of the MD scalar quantizer was computed in [4], for general source densities and m th power distortion measures [13] Perhaps the most interesting case considered here is that of a gaussian density and m = 2. Due to the large number of parameters involved (rates for each of the channels and distortions for all subsets of working nonworking ....

....interesting case considered here is that of a gaussian density and m = 2. Due to the large number of parameters involved (rates for each of the channels and distortions for all subsets of working nonworking channels) comparisons between MD systems can get complicated. However, it is argued in [4] that in the balanced case (i.e. when the rates on both channels are equal) the product d 0 d 1 of the single channel and two channel distortions is a good figure of merit, asymptotically in rate. So, for the gaussian source and m = 2, it was found that there exists a gap of 8.69dB between the ....

J.-C. Batllo and V. A. Vaishampayan. Asymptotic Analysis of Multiple Description Quantizers. IEEE Trans. Inform. Theory, 44(1):278--283, 1998.

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V.A. Vaishampayan and J.-C. Batllo. Asymptotic analysis of multiple description quantizers. IEEE Trans. Information Theory, 44(1):278--284, January 1998.

No context found.

V.A. Vaishampayan and J.-C. Batllo, "Asymptotic analysis of multiple description quantizers," IEEE Trans. Inform. Theory, vol. 44, pp. 278-284, Jan. 1998.

No context found.

V.A. Vaishampayan and J.-C. Batllo. Asymptotic analysis of multiple description quantizers. IEEE Trans. Information Theory, 44(1):278--284, January 1998.

No context found.

V. A. Vaishampayan and J.-C. Batllo, "Asymptotic analysis of multiple description quantizers," IEEE Trans. on Information Theory, vol. 44, no. 1, pp. 278-284, Jan. 1998.

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