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Reviewer: Minette Carl

Coding theory analyzes the transmission of information over noisy communication channels that are not necessarily robust. Time constraints have to be satisfied for efficient digital communication systems, and space constraints in bandwidth for transmission and storage of data. Architectures for implementing both encoding and decoding algorithms are developed in practice for communication systems. This text provides a unified framework for presenting coding theory algorithms, signal processing architectures, and accompanying applications. The book reviews the basics of coding theory before continuing with more advanced block- and cyclic-based codes. Specific coding schemes discussed are algebraic and linear block and cyclic codes (chapter 2), convolutional codes (chapter 3), turbo and low-density parity codes (chapter 4), and space-time codes (chapter 5). Two mathematical appendices (on algebraic structures and linear algebra) are included to ensure that the reader makes the most of the text. The book balances the potentially heavy underlying mathematics with a pleasant presentation style, summarizing the main aspects of the discussions and motivating the issues by providing practical considerations for implementing the coding techniques. As such, the fundamental theoretical approaches are related to applicable coding practices. The book balances the standard coding schemes such as block and convolutional codes, in addition to more advanced coding schemes such as turbo and low-density parity codes (LDPC), discussing relevant research questions involving space and time constraints. These are all presented in a consistent manner, connecting the theories to their applications. Specifically, chapter 1 reviews information theory within communications systems. Topics of concern are the entropy of the information, and the channel capacity of the transmission for simple, binary symmetric, and under additive white Gaussian noise (AWGN) channels. Chapter 2 develops these concepts further with algebraic coding theory. Practical parameters for codes are discussed. Maximum likelihood principles and error-detection properties are incorporated. Linear block codes are explained in detail, including the generator and parity-check matrix, dual codes, and bounds. Similarly, cyclic codes are explained in detail, including the generator and parity-check polynomial, dual codes, linear feedback shift registers (LFSRs), and Reed-Solomon codes. In chapter 3, convolutional codes are developed. The topics considered are constructing the generator matrix in the time domain, and designing the state diagram for a convolutional encoder. The trellis diagram is presented, along with Viterbi's algorithm. Distance properties and error bounds are discussed. Other topics included in this chapter are soft-input decoding (punctured codes), soft-output decoding, and the derivation of a posteriori probability (APP), for regular and log domains, and convolutional coding in mobile communications using a hybrid automatic repeat request (ARQ) over enhanced general packet radio system (EGPRS) modulation and coding. Chapters 4 and 5 present advanced coding techniques. Turbo codes are discussed in chapter 4, starting with codes based on sparse graphs and including those that incorporate a log-likelihood algebra for belief propagation. Code concatenations are implemented as product codes, which are iteratively decoded. For concatenated convolutional codes, serial and parallel concatenations apply. Extrinsic information transfer (EXIT) charts are calculated, and weight distributions (full versus partial) are considered. A variety of woven codes are suggested. Chapter 5 introduces space-time codes. Digital modulation schemes, spatial channels, and ergodic error probabilities all contribute to this method. An orthogonal approach (based on Alamouti's scheme) is considered, with an extension for more than two transmit antennas. Spatial multiplexing is accomplished by iterative APP preprocessing and per-layer decoding. The original Bell Laboratories layered spacetime (BLAST) detection methodology is presented, along with QL Decomposition and interference cancellation techniques. Academicians and those in industry will readily accept this book. It is most suited for graduate or advanced undergraduate students in communication systems, computer science (CS), or engineering. Engineers can also use this work to gain a better understanding of the theoretical foundations of coding theory, and the direct industrial applications for communication systems. Online Computing Reviews Service