This article focuses on the compressed representations of the pictures

The objective of multiple description coding (MDC) is to encode a source into two (or more) bitstreams supporting two quality levels of decoding. A high-quality reconstruction should be decodable from the two bitstreams together, while lower, but still acceptable, quality reconstructions should be decodable from either of the two individual bitstreams. This paper describes techniques for meeting MDC objectives in the framework of standard transform-based image coding through the design of pairwise transforms.

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.

Real-time audio and video data streamed over unreliable IP networks, such as the Internet, may encounter losses due to dropped packets or late arrivals. This paper reviews error-concealment schemes developed for streaming realtime audio and video data over the Internet. Based on their interactions with (video or audio) source coders, we classify existing techniques into source coder-independent schemes that treat underlying source coders as black boxes, and source coder-dependent schemes that exploit coder-specific characteristics to perform reconstruction. Last, we identify possible future research directions. 1. Introduction Increases in bandwidth and computational speed lead to growing interests in real-time audio and video transmissions over the Internet. In the Internet, packets carrying real-time data may be dropped or arrive too late to be useful because the Internet is a packet-switched, best-effort delivery service, with no guarantee on the quality of service (QoS). Traditi...

The high-rate squared-error distortions of a balanced multiple description lattice vector quantizer are analyzed for a memoryless source with probability density function p, differential entropy h(p) ! 1, and lattice codebook . For any a 2 (0; 1) and rate pair (R; R), it is shown that the two-channel distortion d0 and the channel 1 (or channel 2) distortion ds satisfy lim R!1 d02 2R(1+a) = G()2 2h(p) =4 and lim R!1 ds2 2R(1\Gammaa) = G(SL)2 2h(p) ; where G() is the normalized second moment of a Voronoi cell of the lattice and G(SL) is the normalized second moment of a sphere in L dimensions. I. Introduction We consider a two-channel multiple description 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 un...

A high rate analysis is presented for multiple description quantizers introduced in [1], for rth power distortions and general source densities. Both, fixed length and variable length encoding of the quantizer indices are considered. Optimal companding functions are shown to be the same as for single channel quantizers. As compared to the bound in [2], a gap of 8.69 dB and 3.07 dB exists between the entropy-constrained and level-constrained cases, respectively, for a memoryless Gaussian source and r = 2, Index terms: Source Coding, Quantization, Data Compression, Multiple Descriptions, Diversity Systems. This work was was presented in part at the 1994 IEEE International Symposium on Information Theory, Trondheim, Norway, and was supported by grants NSF NCR-9104566 and NSF NCR9314221. This work was performed while the first author was at Texas A&M University. 1 I Introduction We present an asymptotic analysis of multiple description scalar quantizers (MDSQ's), introduced in [1] fo...

Abstract—We consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion profile, ranging from symmetric or balanced to successively refinable. We present a solution to a labeling problem, which is an important part of the construction, along with a general design procedure. The high-rate asymptotic performance of the quantizer is also studied. We evaluate the rate-distortion performance of the quantizer and compare it to known information-theoretic bounds. The high-rate asymptotic analysis is compared to the performance of the quantizer. Index Terms—Cubic lattice, high-rate quantization, lattice quantization, multiple descriptions, quantization, source coding, successive refinement, vector quantization. I.

The problem of designing a multiple description vector quantizer with lattice codebook # is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices A 2 and Z i , i = 1, 2, 4, 8 that make use of this labeling algorithm. The high-rate squared-error distortions for this family of vector quantizers are then analyzed for a memoryless source with probability density function p and di#erential entropy h(p) < #. For any a # (0, 1) and rate pair (R, R), it is shown that the two-channel distortion d 0 and the channel 1 (or channel 2) distortion d s satisfy lim R## d 0 2 2R(1+a) = 1 4 G(#)2 2h(p) and lim R## d s 2 2R(1-a) = G(S L )2 2h(p) , where G(#) is the normalized second moment of a Voronoi cell of the lattice # and G(S L ) is the normalized second moment of a sphere in L dimensions. Index Terms: Source Coding, Quantization...

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In this paper we review error resilience techniques for real-time video transport over unreliable networks. Topics covered include an introduction to today's protocol and network environments and their characteristics, encoder error resilience tools, decoder error concealment techniques, as well as techniques that require cooperation between encoder, decoder and the network. We provide a review of general principles of these techniques as well as specific implementations adopted by the H.263 and MPEG-4 video coding standards. The majority of the paper is devoted to the techniques developed for block-based hybrid coders using motion-compensated prediction and transform coding. A separate section covers error resilience techniques for shape coding in MPEG-4. I. Introduction A. Error Resilience in Video Communications: Importance and Approach A video communications system typically involves five steps, as shown in Figure 1. The video is first compressed by a video encoder to reduce th...