Abstract
A. Summary The basic purpose of data compression is to massage a data stream to reduce the average bit rate required for transmission or storage by removing unwanted redundancy and/or unnecessary precision. A mathematical formulation of data compression providing figures of merit and bounds on optimal performance was developed by Shannon [1,2] both for the case where a perfect compressed reproduction is required and for the case where a certain specified average distortion is allowable. Unfortunately, however, Shannon's probabilistic approach requires advance precise knowledge of the statistical description of the process to be compressed — a demand rarely met in practice. The coding theorems only apply, or are meaningful, when the source is stationary and ergodic. We here present a tutorial description of numerous recent approaches and results generalizing the Shannon approach to unknown statistical environments. Simple examples and empirical results are given to illustrate the essential ideas.
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