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Reviewer: Vladimir Botchev

The first edition of this book [1] is probably one of the most popular books for teaching error correcting coding. It has proven itself as an extremely valuable reference-for teaching classes, self-study, and even software/hardware design-for more than 20 years. Since 1982, error correcting coding has become ubiquitous in everyday products like compact disc (CD) players and broadband modems, and new or revised coding paradigms have entered the scene; it was obvious that a new edition would be more than welcome, specifically, an edition addressing the evolution of the discipline during that time span. Other excellent works on this subject have been published during the last 20 years. None, however, have offered the authors' unique tutorial style and careful presentation, using a generous number of block diagrams, graphs, and step-by-step introductions to key algorithms. In this respect, the new edition doesn't disappoint; the style remains excellent, and the diagrams and graphs are even better. The old topics discussed remain almost unchanged, the coverage of Reed Solomon is slightly expanded, and new or enhanced coverage is included for convolutional coding, trellis coded modulation, turbo coding, low density parity check (LDPC) codes, and the soft decoding of block codes, to cite the most important. The coverage is very detailed; the book has an impressive 1,200-plus page count. Excellent end-of-chapter problems are provided, many with solution hints. A companion Web page is under construction. One could be tempted to give this impressive book the title Bible of error correcting coding theory and practice. In a certain sense, it is, given its broad coverage, detailed examples, and extensive references. Despite all of its qualities, however, certain aspects of the book still leave something to be desired. For example, the ubiquitous cousin of error checking and correcting (ECC), error-detecting cyclic redundancy checking (CRC) coding, is only skimmed over. In a book of this size, I would expect somewhat more detail on CRC. The introduction to finite fields and corresponding arithmetic structures, while excellent, is not changed from the first edition. For example, no explanation is given as to how it happens that extension fields exist for GF(2^m) , or, for that matter, GF(p^m) , where p is prime. They are just said to exist. A demonstration using available tools and concepts from this chapter is totally within reach; a page or two would suffice (like in the excellent book by Pretzel [2]). Reed Solomon codes are essentially codes for correcting burst errors, and they are helped in that by convolutional interleavers (for example, the asymmetric digital subscriber line (ADSL) standard). A page or two would have been enough to introduce this important topic in more detail, yet the authors did not do this. I prefer to keep this list of omissions short, because these details, even if important, can be learned from easily accessible papers and tutorials, and do not really weaken the main text. However, given the book's size, a few more pages wouldn't have hurt the authors or publisher, and would have only been of benefit to the student. There are student reports from classes where this book (in its first edition) is dominantly used that some fine points, especially in Reed Solomon decoding, are just listed, with no proof provided. And very often, when learning a specific discipline, people would like to know the why, not only the how. The situation is better in this edition, however I again found quite inadmissible statements, such as the one on page 210: "The proof of this is quite complicated and is omitted from this introductory book," in reference to the minimum degree error location polynomial satisfying the first M Newton identities, where M is equal to the number of discrepancies plus 1. The proof is indeed involved, but nonetheless within reach given the finite field basics taught as part of this book. There could at least be an appendix, with this (and other) proofs, for students who want to know why, not only how. Who could reasonably expect that, given a manual of this size, the number of such sentences would be virtually zero__?__ That's exactly the approach taken by Rhee, however, in his excellent book [3]. So for proof of the above, turn to Rhee's book, or to the original reference by Peterson and Weldon [4] (not even mentioned in the expression context in this book). Overall, this is an impressive reference for learning error correcting codes. Be warned, however, about surprises when a "Why__?__" question is posed. The answer may very well be missing. Online Computing Reviews Service