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22
Quantized frame expansions with erasures
- Applied and Computational Harmonic Analysis
, 2001
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Generalized multiple description coding with correlating transforms
- IEEE Trans. Inform. Theory
, 2001
"... Abstract—Multiple description (MD) coding is source coding in which several descriptions of the source are produced such that various reconstruction qualities are obtained from different subsets of the descriptions. Unlike multiresolution or layered source coding, there is no hierarchy of descriptio ..."
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Cited by 82 (2 self)
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Abstract—Multiple description (MD) coding is source coding in which several descriptions of the source are produced such that various reconstruction qualities are obtained from different subsets of the descriptions. Unlike multiresolution or layered source coding, there is no hierarchy of descriptions; thus, MD coding is suitable for packet erasure channels or networks without priority provisions. Generalizing work by Orchard, Wang, Vaishampayan, and Reibman, a transform-based approach is developed for producing descriptions of an-tuple source,. The descriptions are sets of transform coefficients, and the transform coefficients of different descriptions are correlated so that missing coefficients can be estimated. Several transform optimization results are presented for memoryless Gaussian sources, including a complete solution of the aP, aPcase with arbitrary weighting of the descriptions. The technique is effective only when independent components of the source have differing variances. Numerical studies show that this method performs well at low redundancies, as compared to uniform MD scalar quantization. Index Terms—Erasure channels, integer-to-integer transforms, packet networks, robust source coding.
The Kadison–Singer problem in mathematics and engineering
- Proc. Natl. Acad. Sci. USA 103 (2006
, 2006
"... Abstract. We will show that the famous, intractible 1959 Kadison-Singer problem in C ∗-algebras is equivalent to fundamental unsolved problems in a dozen areas of research in pure mathematics, applied mathematics and Engineering. This gives all these areas common ground on which to interact as well ..."
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Cited by 68 (19 self)
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Abstract. We will show that the famous, intractible 1959 Kadison-Singer problem in C ∗-algebras is equivalent to fundamental unsolved problems in a dozen areas of research in pure mathematics, applied mathematics and Engineering. This gives all these areas common ground on which to interact as well as explaining why each of these areas has volumes of literature on their respective problems without a satisfactory resolution. In each of these areas we will reduce the problem to the minimum which needs to be proved to solve their version of Kadison-Singer. In some areas we will prove what we believe will be the strongest results ever available in the case that Kadison-Singer fails. Finally, we will give some directions for constructing a counter-example to Kadison-Singer. 1.
Quantized Frame Expansions as Source-Channel Codes for Erasure Channels
- Proc. IEEE Data Compression Conf
, 1999
"... Quantized frame expansions are proposed as a method for generalized multiple description coding, where each quantized coe cient is a description. Whereas previous investigations have revealed the robustness of frame expansions to additive noise and quantization, this represents a new application of ..."
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Cited by 41 (8 self)
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Quantized frame expansions are proposed as a method for generalized multiple description coding, where each quantized coe cient is a description. Whereas previous investigations have revealed the robustness of frame expansions to additive noise and quantization, this represents a new application of frame expansions. The performance of a system based on quantized frame expansions is compared to that of a system with a conventional block channel code. The new system performs well when the number of lost descriptions (erasures on an erasure channel) is hard to predict. 1
Transform Coding with Backward Adaptive Updates
, 1999
"... The Karhunen-Loeve transform (KLT) is optimal for transform coding of a Gaussian source. This is established for all scale invariant quantizers, generalizing previous results. A backward adaptive technique for combating the data-dependence of the KLT is proposed and analyzed. When the adapted transf ..."
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Cited by 28 (5 self)
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The Karhunen-Loeve transform (KLT) is optimal for transform coding of a Gaussian source. This is established for all scale invariant quantizers, generalizing previous results. A backward adaptive technique for combating the data-dependence of the KLT is proposed and analyzed. When the adapted transform converges to a KLT, the scheme is universal among transform coders. A variety of convergence results are proven.
Multiple description perceptual audio coding with correlating transforms
- IEEE Trans. Speech Audio
, 2000
"... Abstract—In audio communication over a lossy packet network, concealment techniques are used to mitigate the effects of lost packets. This concealment is markedly improved if the compressed representation retains redundancy to aid in the estimation of lost information. A perceptual audio coder emplo ..."
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Cited by 17 (2 self)
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Abstract—In audio communication over a lossy packet network, concealment techniques are used to mitigate the effects of lost packets. This concealment is markedly improved if the compressed representation retains redundancy to aid in the estimation of lost information. A perceptual audio coder employing multiple description correlating transforms demonstrates this phenomenon. Index Terms—Audio coding, multiple descriptions, packetized audio, robust communication. I.
Multiple description lattice vector quantization: Variations and extensions
- In Data Compression Conference, Snowbird
, 2000
"... Multiple description lattice vector quantization (MDLVQ) is a technique for two-channel multiple description coding. We observe that MDLVQ, in the form introduced by Servetto, Vaishampayan and Sloane in 1999, is inherently optimized for the central decoder; i.e., for a zero probability of a lost des ..."
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Cited by 14 (3 self)
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Multiple description lattice vector quantization (MDLVQ) is a technique for two-channel multiple description coding. We observe that MDLVQ, in the form introduced by Servetto, Vaishampayan and Sloane in 1999, is inherently optimized for the central decoder; i.e., for a zero probability of a lost description. With a nonzero probability of description loss, performance is improved by modifying the encoding rule (using nearest neighbors with respect to “multiple description distance”) and by perturbing the lattice codebook. The perturbation maintains many symmetries and hence does not significantly effect encoding or decoding complexity. An extension to more than two descriptions with attractive decoding properties is outlined. 1
Joint Decoding of Multiple-Description Network-Coded Data
"... This paper introduces a transmission scheme combining multiple description coding (MDC) and network coding (NC). MDC is performed either either via frame expansion (NC-MDC-F) or via correlating transform (NC-MDC-T). Our aim is to provide alternative solutions to the rank deficiency problem which may ..."
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Cited by 6 (1 self)
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This paper introduces a transmission scheme combining multiple description coding (MDC) and network coding (NC). MDC is performed either either via frame expansion (NC-MDC-F) or via correlating transform (NC-MDC-T). Our aim is to provide alternative solutions to the rank deficiency problem which may be encountered in wireless data multicasting using NC at some receivers with poor channel condition. With NC-MDC-F, the reconstruction is performed via mixed integer quadratic programming (MIQP). With NC-MDC-T, the reconstruction algorithm requires simple Gaussian elimination. In both cases, a good robustness to missing NC packets is observed. When the number of missing packets is small, the NC-MDC-T provides better SNR thanks to a reduction of a part of the quantization noise. The price to be paid is a decreased robustness to missing packets. When the number of lost packets increases, a reconstruction is still possible with the NC-MDC-F for some packets, even if the number of missing packets is larger than n − k, the number of redundancy packets introduced by MDC.
