am 26. August 1999
1. The book is comprehensive. It describes many algorithms, and includes several studies on statistics about text compression and language modeling. It is very good in this respect.
2. Math theory is not approached systematically neither algrebaically. For instance, a proof that arithmetic compression works can take less than a page, and the details given take a lot of space and are not as clear as they could be.
3. Although the book emphasizes the idea of separating the model from the coder, the language used is the C programming language, which imposes severe restrictions to this separation. The model and the coder do not exist as entities on their own, they just have different memory space allocations. Compare this to a reasonably good implementation in a pure object environment, where you can actually model a coder object and a model object.
4. I wrote a final project based on this book consisting of several kinds of compression algorithms with implementations for the course Mathematical Objects in Smalltalk at the University of Buenos Aires.
am 28. Juni 1998
If you're looking for a book that explains how to implement the latest and greatest variation of algorithm X, this isn't the book for you. If you want to understand at a fundamental level *why* compression works, you want to read this.
The book has just the right mix of information theory and application. Everything you need to know to understand compression is here; all the rest is in the details.