Издательство Springer, 2005, -432 pp.
There are, so it is alleged, many ways to skin a cat. There are also many ways to teach coding theory. My feeling is that, contrary to other disciplines, coding theory was never a fully unified theory. To describe it, one can paraphrase what has been written about the Enlightenment: "It was less a determined swift river than a lacework of deltaic streams working their way along twisted channels" (E.
0. Wilson, Consilience, 1999).
The seed of this book was sown in 2000, when I was invited to teach a course on coded modulation at Princeton University. A substantial portion of students enrolled in the course had little or no background in algebraic coding theory, nor did the time available for the course allow me to cover the basics of the discipline. My choice was to start directly with coding in the signal space, with only a marginal treatment of the indispensable aspects of "classical" algebraic coding theory. The selection of topics covered in this book, intended to serve as a textbook for a first level graduate course, reflects that original choice. Subsequently, I had the occasion to refine the material now collected in this book while teaching Master courses at Politecnico di Torino and at the Institute for Communications Engineering of the Technical University of Munich.
While describing what can be found in this book, let me explain what cannot be found. I wanted to avoid generating an omnium-gatherum, and to keep the book length at a reasonable size, resisting encyclopedic temptations. The leitmotiv here is soft-decodable codes described through graphical structures (trellises and factor graphs). I focus on the basic principles underlying code design, rather than providing a handbook of code design. While an earlier exposure to coding principles would be useful, the material here only assumes that the reader has a firm grasp of the concepts usually presented in senior-lever courses on digital communications, on information theory, and on random processes.
Each chapter contains a topic that can be expatiated upon at book length. To include all facts deserving attention in this tumultuous discipline, and then to clarify their finer aspects, would require a full-dress textbook. Thus, many parts should be viewed akin to movie trailers, which show the most immediate and memorable scenes as a stimulus to see the whole movie.
As the mathematician Mark Kac puts it, a proof is that which convinces a reasonable reader; a rigorous proof is that which convinces an unreasonable reader. I assume here that my readers are reasonable, and hence try to avoid excessive rigor at the price of looking sketchy at times, with many treatments that should be taken modulo mathematical refinements.
The reader will observe the relatively large number of epexegetic figures, justified by the fact that engineers are visual animals. In addition, the curious reader may want to know the origin of the short sentences appearing at the beginning of each chapter. These come from one of the few literary works that was cited by C. E. Shannon in his technical writings. With subtle irony, in his citation he misspelled the work's title, thus proving the power of redundancy in error correction. Some sections are marked *. This means that the section's contents are crucial to the developments of this book, and the reader is urged to become comfortable with them before continuing.
Tour d'horizon
Channel models for digital transmission
Coding in a signal space
Fading channels
Trellis representation of codes
Coding on a trellis: Convolutional codes
Trellis-coded modulation
Codes on graphs
LDPC and turbo codes
Multiple antennas
A Facts from information theory
B Facts from matrix theory
C Random variables. vectors. and matrices
D Computation of error probabilities
There are, so it is alleged, many ways to skin a cat. There are also many ways to teach coding theory. My feeling is that, contrary to other disciplines, coding theory was never a fully unified theory. To describe it, one can paraphrase what has been written about the Enlightenment: "It was less a determined swift river than a lacework of deltaic streams working their way along twisted channels" (E.
0. Wilson, Consilience, 1999).
The seed of this book was sown in 2000, when I was invited to teach a course on coded modulation at Princeton University. A substantial portion of students enrolled in the course had little or no background in algebraic coding theory, nor did the time available for the course allow me to cover the basics of the discipline. My choice was to start directly with coding in the signal space, with only a marginal treatment of the indispensable aspects of "classical" algebraic coding theory. The selection of topics covered in this book, intended to serve as a textbook for a first level graduate course, reflects that original choice. Subsequently, I had the occasion to refine the material now collected in this book while teaching Master courses at Politecnico di Torino and at the Institute for Communications Engineering of the Technical University of Munich.
While describing what can be found in this book, let me explain what cannot be found. I wanted to avoid generating an omnium-gatherum, and to keep the book length at a reasonable size, resisting encyclopedic temptations. The leitmotiv here is soft-decodable codes described through graphical structures (trellises and factor graphs). I focus on the basic principles underlying code design, rather than providing a handbook of code design. While an earlier exposure to coding principles would be useful, the material here only assumes that the reader has a firm grasp of the concepts usually presented in senior-lever courses on digital communications, on information theory, and on random processes.
Each chapter contains a topic that can be expatiated upon at book length. To include all facts deserving attention in this tumultuous discipline, and then to clarify their finer aspects, would require a full-dress textbook. Thus, many parts should be viewed akin to movie trailers, which show the most immediate and memorable scenes as a stimulus to see the whole movie.
As the mathematician Mark Kac puts it, a proof is that which convinces a reasonable reader; a rigorous proof is that which convinces an unreasonable reader. I assume here that my readers are reasonable, and hence try to avoid excessive rigor at the price of looking sketchy at times, with many treatments that should be taken modulo mathematical refinements.
The reader will observe the relatively large number of epexegetic figures, justified by the fact that engineers are visual animals. In addition, the curious reader may want to know the origin of the short sentences appearing at the beginning of each chapter. These come from one of the few literary works that was cited by C. E. Shannon in his technical writings. With subtle irony, in his citation he misspelled the work's title, thus proving the power of redundancy in error correction. Some sections are marked *. This means that the section's contents are crucial to the developments of this book, and the reader is urged to become comfortable with them before continuing.
Tour d'horizon
Channel models for digital transmission
Coding in a signal space
Fading channels
Trellis representation of codes
Coding on a trellis: Convolutional codes
Trellis-coded modulation
Codes on graphs
LDPC and turbo codes
Multiple antennas
A Facts from information theory
B Facts from matrix theory
C Random variables. vectors. and matrices
D Computation of error probabilities