In this work, the authors have attempted to provide a critique of differential-predictive coding (DPC), based on a model of recursive coding. Given the narrow focus of this work, it should be considered a monograph. The book has a strong theoretical flavor and is unlikely to be of interest to implementors. A substantial acquaintance with the theory and literature in the field is assumed. The writing style is dense, and the book is not easy reading for the nonexpert. The model used is the Fine-McMillan model of recursive quantization, which seems general enough to include many existing designs. This model is introduced in chapter 1 along with a statement of the design problem for recursive quantizers (RQs). Chapter 2 investigates the structural and design problems of RQs. The theoretical development is interspersed with a lot of examples analyzing RQs described in the literature. The framework of chapter 1 is used in these analyses. Chapter 3 embeds DPC in the Fine-McMillan model. It provides an extended discussion of the predictor-corrector model and points out that minimizing distortion is not the same as minimizing predictor-distortion--a major conclusion of this work. It is to be noted that most practical designs assume that these two minimizations are indeed equivalent. Chapter 4 provides some design examples to illustrate the material presented in the previous chapters. The book also includes a good bibliography with 113 references. There is no index.

A good contribution of this work is the introduction of a framework for the systematic investigation of RQs. While the authors have analyzed many existing designs, they also point out a lot of hard problems that are still open, for example, the design of strongly optimal RQs.

This book should appeal to researchers. Some conclusions that may be of use to designers are scattered throughout the text. Perhaps a section that gathers these conclusions in one place and discusses their implication to designers would be useful. The lack of such a section is rather unfortunate, since some of the conclusions should provide food for thought for designers, for example, the result that, under certain conditions, the predictor in the predictor-corrector model is super- fluous and only a corrector is needed. This is to be contrasted with the increasing complexity of prediction-error coding tools in practice. The examples in chapter 4 are for illustrative purposes only and are not very practical. The comparison of different approaches is of subjective quality. This may be understandable given the paucity of objective standards of comparison in the field, but it is unlikely to win many converts.

There are not many typos but unfortunately some of them confuse the reader--in the definition of the Fine-McMillan model on page 4, :3K-X-_n(i) should read :3K-X-_n(i) as it is in the rest of the text.