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Reviewer: Vladimir Botchev

Many books on error correction coding exist. Some have a more theoretical focus, and others focus on practical implementations. Rarely, however, do texts provide both theoretical depth and strong practical constructs. This is one of these rare texts; it would hardly be an overstatement to regard this book as one of the best, if not the best, of its kind. The book covers both classical methods, such as block and convolutional codes, and modern developments, such as turbo codes and low-density parity check (LDPC) codes (LDPC codes have been known for decades, but only recently, thanks to technological advances, have they started to be considered for practical implementations). The author provides detailed proofs for almost every theorem or lemma he introduces. This is in contrast with, for example, Lin and Costello's book [1] (the error correction coding bible), where the reader is shielded from some proofs and developments. A unique feature of the book is the way the relevant mathematical structures and developments are introduced. This is done in a distributed manner, which is to say that most of the mathematical derivations are not lumped together in a chapter or two, but are delivered throughout all of the chapters. This style of presentation is very helpful for self-study. Another unique feature is the collection of lab works, where, with the help of an impressive amount of MATLAB C/C++ code (all available on the book's Web site), the student can obtain real-world experience, and deal with the intricacies of programming for error control coding. The lab descriptions are very detailed, and require good programming skills. Numerous end-of-chapter problems also make this book quite attractive for self-study. These are very carefully crafted, and the attentive reader will undoubtedly discern the different levels of difficulty the exercises are designed with, and will thus test his or her current level of understanding by climbing this exercise ladder. The book consists of 17 chapters, grouped into five parts. Part 1 contains only the first introductory chapter. In this chapter, the motivation for designing and using error correcting codes is given, in the context of information theory and communications. The chapter ends with the first lab, consisting of a simulation of a communication channel. The ten chapters of Part 2 are devoted to block codes. In the first of these ten chapters, basic notions of abstract algebra are introduced. The next chapter continues with an introduction of the simplest linear block codes, namely, Hamming codes. A detailed chapter on rings, polynomials, and the principles of cyclic encoding follows. This chapter ends with two labs, for polynomial division and linear-feedback shift register (LFSR), and the ubiquitous cyclic redundancy check (CRC). A very good introduction to number theory is provided in chapter 5, which is also followed by two labs, on programming the Euclidean algorithm and on performing Galois field arithmetic. Chapter 6 is the cornerstone cyclic block code chapter, since it addresses Reed Solomon (RS) codes (and Bose-Chaudhuri-Hocquenghem (BCH) codes, of course). This chapter is an extremely well-written account of cyclic block codes, and almost no theorem introduced is left without a proof. Three labs end the chapter, one on programming the Berlekamp-Massey algorithm, and the remaining two on BCH and Reed Solomon decoding. Chapter 7 continues with Reed Solomon decoding, by revealing alternate approaches to decoding. Chapter 8 introduces other important block codes, such as Reed-Muller and Golay codes. Chapter 9 is more abstract, and is mostly information theory oriented; it addresses bounds on codes, for example the Varshamov bound. Chapter 10 briefly tackles the important question of burst error channel and interleavers for block codes. As an example, the compact disk interleaved RS decoder is presented. Part 2 ends by discussing some new methods for the soft decoding of block codes. Part 3 contains two chapters, and is entirely concerned with convolutional codes and trellis-coded modulation. The presentation is less detailed than for block codes, perhaps to limit the size of the book. There are three labs in this part: two on convolutional encoding and the Viterbi algorithm, and one on the trellis coder/decoder (codec). Part 4 is a thorough introduction to turbo and LDPC codes. Precious practical information is again provided in the two labs in this part, on programming a turbo decoder and an LDPC decoder. This part ends with a brief account of decoding algorithms on graphs. Part 5 consists of only the last chapter, and addresses the particular types of concepts and codes for fading radio frequency (RF) channels, the space-time codes. A short appendix on log-likelihood algebra ends the book. In conclusion, it must be said that this is not an easy book-no serious book on error coding is. The presentation and clarity of the explanations make this work one of the best error control coding books on the market. I highly recommended it for both academic study and practical reference. Even people not directly involved in designing error correction codecs will benefit from the book's style and clarity, and can use it to increase the breadth of their knowledge. Online Computing Reviews Service