Rate-distortion theory is the branch of information theory that treats compressing the data produced by an information source down to a specified encoding rate that is strictly less than the source's entropy This necessarily entails some lossiness, or distortion, between the original source data and the best approximation thereto that can be produced on the basis of the encoder's output bits Rate-distortion theory was introduced in the seminal works written in 1948 and 1959 by C E Shannon, the founder of information theory We describe Shannon's contribution and then trace its subsequent development worldwide Heavier than usual emphasis is placed on the concept of “matching” a channel to a source in the rate-distortion sense, and also on the analogous matching of a source to a channel Experimental evidence has been mounting in support of the hypothesis that living organisms often simultaneously achieve both of these matchings when processing their sensory inputs, thereby eliminating the need for the complex encoding and decoding operations that are needed in order to produce an information-theoretically optimum system in the absence of such double matching


Keywords:

rate-distortion;
lossy source coding;
distortion measure;
Shannon;
joint source-channel coding;
bioinformation theory

Rate-Distortion Theory

We consider the problem of separate coding for two correlated memoryless Gaussian source. We determine the rate-distortion region in a special case that one source plays a role of partial side information to reproduce sequences emitted from the other source with a prescribed average distortion level. We also derive an explicit outer bound of the rate-distortion region, demonstrating that the inner bound obtained by Berger (1978) partially coincides with the rate-distortion region.

/pdf/gaussian-multiterminal-source-coding-23khvc5jd9.pdf

Gaussian multiterminal source coding

A brief chronicle is given of the historical development of the central problems in the theory of fundamental limits of data compression and reliable communication.

/pdf/fifty-years-of-shannon-theory-t0i0ucf5tb.pdf

Fifty years of Shannon theory

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.

Lossy source coding

A unified framework is given for multiple user information networks. These networks consist of several users communicating to one another in the presence of arbitrary interference and noise. The presence of many senders necessitates a tradeoff in the achievable information transmission rates. The goal is the characterization of the capacity region consisting of all achievable rates. The focus is on broadcast, multiple access, relay, and other channels for which the recent theory is relativdy well developed. A discussion of the Gaussian version of these channels demonstrates the concreteness of the encoding and decoding necessary to achieve optimal information flow. We also offer speculations about the form of a general theory of information flow in networks.

Multiple user information theory

An upper bound on the rate distortion function is obtained for source coding with partial side information at the decoder. Previous results were for complete side information, i.e. full knowledge of Y_{n} . below. A diagram given in the paper helps to describe the problem. The bound is given in

An upper bound on the rate distortion function for source coding with partial side information at the decoder

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An upper bound on the rate distortion function for source coding with partial side information at the decoder