J.-C. Batllo and V.A. Vaishampayan. Asymptotic performance of multiple description transform codes. IEEE Trans. Information Theory, 43(2):703-- 707, March 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of memoryless sources or sources with finite memory. In [18] Ingle et al. consider the problem of designing DPCM systems for MD coding of sources with memory. Batllo et al. considered a similar problem and proposed a solution that combines the use of an orthogonal block transform and of the MDSQ [2]. As in the memoryless case, this system has some good asymptotic properties. At low rates, however, except for some practical results obtained in the context of still image coding [24] much less is known. Note that Batllo and Vaishampayan use the term Multiple Description Transform Coder (MDTC) ....

....[32] This different approach leads to a different formulation of the optimization problem and, in our case, to the analytical solution presented in Theorem 2, which is not present in [34] In Section 4 we assess the performance of our system. We compare it against the ideal bounds, the MDTC [2] and the MD DPCM system [18] For this comparison we consider two possible scenarios. The first one is high rates and infinite delay complexity. This first comparison is interesting because it is under these hypotheses that the optimization problem is stated and solved both in [2] and in this ....

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J.-C. Batllo and V.A. Vaishampayan. Asymptotic performance of multiple description transform codes. IEEE Trans. Information Theory, 43(2):703--707, March 1997.

....there are only three useful operating points. Fig. 4(b) clearly indicates the deficiency of UMDSQ in providing useful operating points for low base rates and redundancies. Applications of MDSQ are described in [7] 37] 10] Joint optimization of an orthogonal transform and MDSQ is discussed in [38]. For the purposes of this paper, it is sufficient to note that an identity transform is optimal for a source vector with independent components. Note that Batllo and Vaishampayan use the term multiple description transform coding (MDTC) to refer to MDSQ applied to coefficients from an orthogonal ....

....points. Only the useful ones are shown; those with average side distortion per component more than (a a) 2 are discarded, as are those strictly worse than any other operating point. This strategy is essentially prescribed by the theory since using no transform is optimal according to [38]. Theorem I does not directly give us performance bounds for the sources that we consider. However, it does give bounds to apply separately to each component. The approximate bounds shown in Fig. 11 are obtained by fixing the central distortion for each component to match that of the other ....

J.-C. Batllo and V. A. Vaishampayan. Asymptotic performance of multiple description transform codes. IEEE Trans. Inform. Th., 43(2):703707, March 1997.

....is reduced in this experiment to 3.10dB. So in this case the filter bank system could effectively compete with Multiple Description Transform codes based on decorrelating the input sequence with a unitary transform and then in applying a different MD Scalar Quantizer on each decorrelated component [1]. An important question raised by our work relates to trade offs between coding performance and delay complexity of the encoders. The filters obtained with our proposed design procedure are in general of infinite length, but in practical settings, we may be forced to consider approximate FIR ....

....and (b) the identification of conditions (i.e. 9 MD coding of highly correlated sources) under which subspace based methods are potentially competitive with quantizer based methods. This is important because, in the context of scalar quantization, MD transform codes attain optimal performance [1]. ....

J.-C. Batllo and V.A. Vaishampayan. "Asymptotic Performance of Multiple Description Transform Codes," IEEE Trans. Inform. Theory, 43(2):703-707, 1997.

....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 been successfully analyzed or designed using the tools described here. Examples which we would have included had time, space, and patience been more plentiful ....

J.-C. Batllo and V. A. Vaishampayan, "Asymptotic performance of multiple description codes," IEEE Trans. Inform. Theory, vol. 43, pp. 703--707, March 1997.

....The technique we develop is based on square, linear transforms and simple scalar quantization, and the design of the transform is paramount. Rather dissimilar methods have been developed which use nonsquare transforms [5] The problem could also be addressed with an emphasis on quantizer design [6, 7]. 2 Proposed Coding Structure Since the source is jointly Gaussian, we can assume without loss of generality that the components are independent. If not, one can use a Karhunen Lo eve transform of the source at the encoder and the inverse at each decoder. We propose the following steps for ....

J.-C. Batllo and V. A. Vaishampayan. Asymptotic performance of multiple description transform codes. IEEE Trans. Info. Theory, 43(2):703--707, 1997.

....) The first design algorithm for practical MD coding was given by Vaishampayan [1] Vaishampayan s approach was based on scalar quantization with the MD property. Though MD scalar quan M. Vetterli is also with the Univ. of California, Berkeley. tizers can be used in conjunction with transforms [2], the first successful attempts to use transforms to obtain the MD property were reported in [3, 4] For backgroundon the MD problem, see [1] and the references therein. The aforementioned techniques are specific to the twochannel MD problem where all, half, or none of the bits make it to the ....

J.-C. Batllo and V. A. Vaishampayan. Asymptotic performance of multiple description transform codes. IEEE Trans. Inform. Th., 43(2):703--707, 1997.

....literature. Rate distortion theoretic results on MDC of memoryless sources are presented in [1] and [2] Vaishampayan presents a method of implementing MDC using scalar quantizers (Multiple Description Scalar Quantizer or MDSQ) in [3] Multiple Description Transform Coding (MDTC) is introduced in [4] and rate distortion theoretic results for sources with memory are presented in this context. Recent work in this area includes [5] and [6] which use pair wise correlating transforms to introduce dependenciesbetween two descriptions transmitted over different channels. Reconstructing a source with ....

....the central distortion decreases at the expense of increased side distortion. Setting a close to 0 maximizes redundancy with the limiting case corresponding to duplication of information over the two streams. In our work, we avoid the constraints imposed by block based MDC approaches(such as in [4] and [5] by allocating rates and redundancies to the classified subbands of an image, subject to overall restrictions on the coding rate and side distortion. A subbanddecomposition provides a layered representation of a source. When MDC is applied to the subbands, it is possible to introduce ....

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J.-C. Battlo and V. Vaishampayan, "Asymptotic Performance of Multiple Description Transform Codes," IEEE Transactions on Information Theory," vol. 43, No. 2, pp. 703-707, March 1997.

....subset is acceptable, and that better quality is obtained by more descriptions. It is assumed in MDC that losses to different descriptions are uncorrelated, and that the probability of losing all the descriptions is small. MDC has been implemented in several ways. In the scalar quantizer approach [6, 52, 67, 68, 69], optimal index assignments are hard to find in real time, and suboptimal approaches, such as A2 index assignment [67] introduce a large overhead in bit rate [76] Instead of putting each pixel in every description, a pair wise correlatingtransform (PCT) 45, 75] approach has been proposed to ....

J. C. Batllo and V. A. Vaishampayan. Asymptotic performance of multiple description transform codes. IEEE Trans. on Information Theory, 43:703-707, Mar. 1997.

....a codec which is suitable for use over channels with bursty errors. Such channels include wireless channels which suffer from fading and ATM networks which suffer from cell loss. For protection against bursty errors, the codec uses a diversity method in the form of multiple description codes [7, 8, 2]. In multiple description codes, it is assumed that two independent channels (channel 1 and channel 2) connecting the sender and the receiver are available. Each channel may be in a working or non working state. This information is available to the decoder (possibly through error detection) but ....

J.-C Batllo and V. A. Vaishampayan. Asymptotic performance of multiple description transform codes. IEEE Trans. on Information Theory, 43(2):703--707, March 1997.

....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 been successfully analyzed or designed using the tools described here. Examples which we would have included had time, space, and patience been more plentiful ....

J.-C. Batllo and V. A. Vaishampayan, "Asymptotic performance of multiple description codes," IEEE Trans. Inform. Theory, vol. 43, pp. 703--707, March 1997.

....perspective in [1] and [2] and rate distortion bounds were derived for memoryless sources. A practical method of implementing MDC using scalar quantizers (Multiple Description Scalar Quantizer or MDSQ) is presented in [3] Multiple Description Transform Coding (MDTC) is introduced in [4] and rate distortion theoretic results for sources with memory are presented in this context. Conventionally, MDC has been investigated only from the perspective of transmission over on off channels, i.e, channels which either transmit noiselessly, or fail completely. In [5] Yang and Vaishampayan ....

J-C. Battlo and V.A. Vaishampayan, "Asymptotic performance of multiple description transform codes," IEEE Transactions on Information Theory, vol. IT-43, no. 2, March 1997.

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J.-C. Batllo and V. Vaishampayan, "Asymptotic Performance of Multiple Description Transform Codes," IEEE Transactions on Information Theory, vol. 43, No. 2, pp. 703-707, March 1997.

....Vaishampayan proposed a method for structuring the index information of a standard scalar quantizer for meeting MDC objectives [4] Originally, this idea was applied to code the signal samples directly. Later, it was extended for coding the transform coefficients in a block transform coder [5]. More recently, Servetto et al. have considered its application in wavelet based image coders [6] In another approach [7] Ingle and Vaishampayan modified standard DPCM coding to meet MDC objectives. Whereas the optimal DPCM coder should select a prediction filter that whitens the prediction ....

J.-C. Batllo and V. Vaishampayan, "Asymptotic performance of multiple description transform codes," IEEE Transactions on Information Theory,vol. 43, No. 2, pp. 703-707, March 1997.

....whether these quantizers can be used in practical, low rate scenarios. Further motivation for the use of MDSQs in the specific case of images is provided by the fact that, asymptotically at high rates, good transforms to use in a SD image coder are also good transforms to use in a MD image coder [1]. In this work we show, for the first time, very competitive coding performance for a real source in the low bitrate regime; we thus provide evidence of the usefulness of the MD quantizers even when the high rate assumptions made in their design are clearly violated. The rest of this paper is ....

J.-C. Batllo and V. Vaishampayan. Asymptotic Performance of Multiple Description Transform Codes. IEEE Transactions on Information Theory, 43(2):703--707, March 1997.

....can be used in typical medium to low rate regimes. Further motivation for the use of MD scalar quantizers in the speci c case of images is provided by the fact that, asymptotically at high rates, good transforms to use in a single description coder are also good transforms to use in a MD coder [3]. In this work we show the feasibility of MD scalar quantizers, for a real source (i.e. images) and in the medium to low bit rate regime, thus providing strong support for the usefulness of these quantizers even when the high rate assumptions made in their design are relaxed. The rest of this ....

....the information regarding sets of coecients is deduced only from data causally available at the decoder, so that no explicit map bits are required. 2.1. 2 Issues in the Generation of Two Descriptions To perform MD coding of images, we use the standard MD transform coding architecture proposed in [3], consisting of replacing the single description quantizer with a MD quantizer, and then performing entropy coding of the two output quantized streams independently. This architecture is illustrated in Fig. 1. Entropy Coding Entropy Coding Decorrelating Transform Quantization Description ....

[Article contains additional citation context not shown here]

J.-C. Batllo and V. A. Vaishampayan. Asymptotic Performance of Multiple Description Transform Codes. IEEE Trans. Inform. Theory, 43(2):703-707, 1997.

....can be used in typical medium to low rate regimes. Further motivation for the use of MD scalar quantizers in the specific case of images is provided by the fact that, asymptotically at high rates, good transforms to use in a single description coder are also good transforms to use in a MD coder [3]. In this work we show the feasibility of MD scalar quantizers, for a real source (i.e. images) and in the medium to low bitrate regime, thus providing strong support for the usefulness of these quantizers even when the high rate assumptions made in their design are relaxed. The rest of this ....

....by Ozarow s result 2 . For the creation of more than two descriptions, Berger Wolf and Reingold [6] generalize the construction of index assignments proposed in [35] from two dimensional matrices to arbitrary k dimensional tensors. For coding sources with memory, Batllo and Vaishampayan [3] constructed MD Transform Codes, using the MD quantizer. Their main result is that, for stationary Gaussian sources, both the optimal transform and the optimal bit allocation are identical to 1 Practical in the sense that previous work had focused on the characterization of the MD ....

[Article contains additional citation context not shown here]

J.-C. Batllo and V. A. Vaishampayan. Asymptotic Performance of Multiple Description Transform Codes. IEEE Trans. Inform. Theory, 43(2):703--707, 1997.

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J.-C. Batllo and V.A. Vaishampayan. Asymptotic performance of multiple description transform codes. IEEE Trans. Information Theory, 43(2):703-- 707, March 1997.

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J.-C. Batllo and V.A. Vaishampayan. Asymptotic performance of multiple description transform codes. IEEE Trans. Information Theory, 43(2):703--707, March 1997.

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J.-C. Batllo and V.A. Vaishampayan. "Asymptotic Performance of Multiple Description Transform Codes," IEEE Trans. Inform. Theory, 43(2):703-707, 1997.

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J. C. Batllo and V. A. Vaishampayan, "Asymptotic performance of multiple description transform codes," to appear in IEEE Trans. Info. Theo.

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Battlo J.-C. and Vaishampayan V.A., Asymptotic Performance of Multiple Description Transform Codes, IEEE Transactions on Information Theory,vol. 43, pp. 703706, March 1997.

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J.-C. Batllo and V.A. Vaishampayan, "Asymptotic performance of multiple description transform codes," IEEE Trans. Inform. Theory, vol. 43, no. 2, pp. 703-707, Mar. 1997.

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J.-C. Batllo and V.A. Vaishampayan. Asymptotic performance of multiple description transform codes. IEEE Trans. Information Theory, 43(2):703-- 707, March 1997.

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