This paper places frames in a new setting, where some of the elements are deleted. Since proper subsets of fi'ames are sometimes them- selves frames, a quantized frame expansion can be a useful representation even when some transform coefficients are lost in transmission. This yields robustness to losses in packet networks such as the Internet

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.

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

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.

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.

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. Permission to publish this abstract separately is granted. EDICS Category: SA 2.5 Corresponding author: Jelena Kovacevi'c e-mail: jelena@bell-labs.com Room 2C-176, Bell Labs voice: +1 908-582-6504 600 Mountain Avenue fax: +1 908-582-3340 Murray Hill, NJ 07974 This work was completed while the first author was a consultant at Bell Labs. Submitted as a correspondence item (revised from an August 1998 submission). May 6, 1999 Submitted to IEEE Trans. Speech & Audio Proc. 2 AREAN, KOVA CEVI ' C & GOYAL: MULTIPLE DESCRIPTION PERCEPTUAL AUDIO CODING I. Introduction Most state-of-the-art audio coders combine source coding prin...

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

Multiple description codes generated by quantized frame expansions have been shown to perform well on erasure channels when compared to traditional channel codes. In this paper we propose a multiple description image coding scheme in the wavelet domain using quantized frame expansions. We form zerotrees from wavelet coefficients and apply a tight frame operator to the zerotrees. We then group appropriate expansions to form packets and evaluate the performance of the scheme over an erasure channel. We compare the performance of the proposed scheme with a conventional channel coding scheme. 1.

Multiple description coding (MDC) recently appeared as a joint source-channel coding technique specifically designed for realtime multimedia applications over best effort switched packet networks such as Internet, in order to cope with packet losses due to transmission errors or network congestion. In this paper we compare several redundant wavelet decompositions in the framework of multiple description of scalable video coding. A special attention is paid to the optimal design of the central decoder. Simulation results are provided for motion-compensated filter banks so as to evaluate the efficiency of the central and lateral decoding strategies. Compared with other techniques, a key factor of the proposed analysed schemes is their reduced redundancy factor. 1.

this paper uses a merge operator to modify the tree structure and move on the complexitydistortion curve. This operator does not change the rate of the quantizer, so the complexity-distortion ratio can be tuned independently.