The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analog-to-digital conversion was first recognized during the early development of pulsecode modulation systems, especially in the 1948 paper of Oliver, Pierce, and Shannon. Also in 1948, Bennett published the first high-resolution analysis of quantization and an exact analysis of quantization noise for Gaussian processes, and Shannon published the beginnings of rate distortion theory, which would provide a theory for quantization as analog-to-digital conversion and as data compression. Beginning with these three papers of fifty years ago, we trace the history of quantization from its origins through this decade, and we survey the fundamentals of the theory and many of the popular and promising techniques for quantization.

This article focuses on the compressed representations of the pictures

In just a few years the "Internet Multicast Backbone", or MBone, has risen from a small, research curiosity to a large scale and widely used communications infrastructure. A driving force behind this growth was our development of multipoint audio, video, and shared whiteboard conferencing applications that are now used daily by the large and growing MBone community. Because these real-time media are transmitted at a uniform rate to all the receivers in the network, the source must either run below the bottleneck rate or overload portions of the multicast distribution tree. In this dissertation, we propose a solution to this problem by moving the burden of rate-adaptation from the source to the receivers with a scheme we call Receiver-driven Layered Multicast, or RLM. In RLM, a source distr...

What makes a source-channel communication system optimal? It is shown that in order to achieve an optimal cost--distortion tradeoff, the source and the channel have to be matched in a probabilistic sense. The match (or lack of it) involves the source distribution, the distortion measure, the channel conditional distribution, and the channel input cost function. Closed-form necessary and sufficient expressions relating the above entities are given. This generalizes both the separation-based approach as well as the two well-known examples of optimal uncoded communication. The condition of

We consider the problem of coding images for transmission over error-prone channels. The impairments we target are transient channel shutdowns, as would occur in a packet network when a packet is lost, or in a wireless system during a deep fade: when data is delivered it is assumed to be error-free, but some of the data may never reach the receiver. The proposed algorithms are based on a combination of multiple description scalar quantizers with techniques successfully applied to the construction of some of the most ecient subband coders. A given image is encoded into multiple independent packets of roughly equal length. When packets are lost, the quality of the approximation computed at the receiver depends only on the number of packets received, but does not depend on exactly which packets are actually received. When compared with previously reported results on the performance of robust image coders based on multiple descriptions, on standard test images, our coders attain s...

Abstract—We provide an overview of an architecture of today’s Internet streaming media delivery networks and describe various problems that such systems pose with regard to video coding. We demonstrate that based on the distribution model (live or on-demand), the type of the network delivery mechanism (unicast versus multicast), and optimization criteria associated with particular segments of the network (e.g., minimization of distortion for a given connection rate, minimization of traffic in the dedicated delivery network, etc.), it is possible to identify several models of communication that may require different treatment from both source and channel coding perspectives. We explain how some of these problems can be addressed using a conventional framework of temporal motion-compensated, transform-based video compression algorithm, supported by appropriate channel-adaptation mechanisms in client and server components of a streaming media system. Most of these techniques have already been implemented in RealNetworks ® RealSystem ® 8 and its RealVideo ® 8 codec, which we are using throughout the paper to illustrate our results. Index Terms—Internet media delivery networks, scalable video coding, streaming media, video compression. I.

Lossy coding of speech, high-quality audio, still images, and video is commonplace today. However, in 1948, few lossy compression systems were in service. Shannon introduced and developed the theory of source coding with a fidelity criterion, also called rate-distortion theory. For the first 25 years of its existence, rate-distortion theory had relatively little impact on the methods and systems actually used to compress real sources. Today, however, rate-distortion theoretic concepts are an important component of many lossy compression techniques and standards. We chronicle the development of rate-distortion theory and provide an overview of its influence on the practice of lossy source coding. Index Terms---Data compression, image coding, speech coding, rate distortion theory, signal coding, source coding with a fidelity criterion, video coding. I.

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 heterogeneity of the Internet's transmission resources and end system capability makes it difficult to agree on acceptable traffic characteristics among the multiple receivers of a multicast video stream. Three basic approaches have been proposed to deal with this problem: 1) multicasting of replicated video streams at different rates, 2) multicasting the video encoded in cumulative layers, and 3) multicasting the video encoded in non-cumulative layers. Even though there is a common belief that the layering approach is better than the replicated stream approach, there has been no studies that compare these schemes. This paper is devoted to such a systematic comparison. Our starting point is an observation (substantiated by results in the literature) that a bandwidth penalty is incurred by encoding a video stream in layers. We argue that a fair comparison of these schemes needs to take into account this penalty as well as the specifics of the encoding used in each scheme, protocol complexity, and the topological placement of the video source and the receivers relative to each other. Our results show that the believed superiority of layered multicast transmission relative to stream replication is not as clear cut as is widely believed and that there are indeed scenarios where replication is the preferred approach.

In this paper, an experimental study of the statistical properties of wavelet coefficients of image data is presented, as well as the design of two different morphology-based image coding algorithms that make use of these statistics. A salient feature of the proposed methods is that, by a simple change of quantizers, the same basic algorithm yields high performance embedded or fixed rate coders. Another important feature is that the shape information of morphological sets used in this coder is encoded implicitly by the values of wavelet coefficients, thus avoiding the use of explicit and rate expensive shape descriptors. These proposed algorithms, while achieving nearly the same objective performance of state-of-the-art zerotree based methods, are able to produce reconstructions of a somewhat superior perceptual quality, due to a property of joint compression and noise reduction they exhibit.