1 The Fine-McMillan Recursive Quantizer Model.- 1.1 Source, Channel, Reproduction.- 1.2 The Linear Deltamodulator.- 1.3 The Definition of a Fine-McMillan Recursive Quantizer.- 1.4 The Design Problem.- 1.5 The Simple Quantizer.- 1.6 Theoretical Limits with Given Channel Capacity.- 2 Structural and Design Problems of a Recursive Quantizer.- 2.1 The McMillan Structure Problem.- 2.2 Fine's Principle of Minimum Search.- 2.3 The Principle of Minimum Search and the Property of Equimemory.- 2.4 Optimality and the EM Property-the McMillan Structure Theorem.- 2.5 Strong-optimality, MS and EM Properties-the Reformulation of the McMillan Structure Theorem.- 2.6 The Proof of the Structure Theorem.- 2.7 Feed-forward Design for the Causal Case.- 2.8 Trellis Coders in Delayed Recursive Quantizers.- 3 Differential Predictive Quantizers.- 3.1 Additive Decoding.- 3.2 Additive Decoding, MS and EM Properties-the Definition of the Differential Predictive Quantizer.- 3.3 A Misunderstanding Concerning the Predictor.- 3.4 Additive Decoding and the Feed-forward Principle.- 4 Design Examples-Speech Compression.- 4.1 The Stationary Model of Speech.- 4.2 The Design of a DPC.- 4.3 The Design of a Fine-McMillan Type RQ.- References.- Appendix 1.- Appendix 2.- Appendix 3.
The spreading of digital technology has resulted in a dramatic increase in the demand for data compression (DC) methods. At the same time, the appearance of highly integrated elements has made more and more com plicated algorithms feasible. It is in the fields of speech and image trans mission and the transmission and storage of biological signals (e.g., ECG, Body Surface Mapping) where the demand for DC algorithms is greatest. There is, however, a substantial gap between the theory and the practice of DC: an essentially nonconstructive information theoretical attitude and the attractive mathematics of source coding theory are contrasted with a mixture of ad hoc engineering methods. The classical Shannonian infor mation theory is fundamentally different from the world of practical pro cedures. Theory places great emphasis on block-coding while practice is overwhelmingly dominated by theoretically intractable, mostly differential predictive coding (DPC), algorithms. A dialogue between theory and practice has been hindered by two pro foundly different conceptions of a data source: practice, mostly because of speech compression considerations, favors non stationary models, while the theory deals mostly with stationary ones.
Springer Book Archives