Название: Channel Coding
Автор: Werner Henkel
Издательство: Springer
Серия: Signals and Communication Technology
Год: 2026
Страниц: 450
Язык: английский
Формат: pdf (true), epub
Размер: 50.8 MB

This book offers an extensive guide to classical and modern coding theory. Mainly addressed to graduate students, scientists and engineers, it may also be used to teach advanced undergraduates. It starts with an introduction to channels, metrics, and information theory fundamentals providing the essential background to understand the more advanced topics covered later. The core of the book offers a complete treatment of block and convolutional codes, including important decoding algorithms. Coding types are described together with the corresponding coded modulation and shaping methods. Trellises for block codes are introduced as well as modern coding schemes such as Turbo, LDPC, and Polar Codes. Network coding and lattices are also briefly described. Finally, this book also includes an extensive set of exercises, questions, and solutions, which will facilitate understanding and self-learning.

Channel coding provides error protection by means of a suitable addition of redundancy to the signal or data. At first sight, this is counterproductive to Source Coding. Source coding eliminates less structured redundancy, whereas channel coding adds redundancy in such a structured way that it allows for error detection and correction. The different algorithms for channel coding will be treated in this book. We divide into block- and sequence-based methods, i.e., block and convolutional codes.

Chapters 1 and 2 provide introductory material talking about channels and metrics as well as the essential information theoretic background, respectively. It can, of course, not be a complete information theory treatment. Hereto, we recommend a separate course based on typical IT books, just as the ones by Cover and Thomas or Csiszár and Körner.
Thereafter, the book first follows the traditional block and convolutional code separation to finally dissolve the strict separation. We start with simple block codes and essential definitions in Chap. 3, immediately moving over to Convolutional Codes in three Chapters, deferring the required mathematics for algebraic block codes to a later chapter.
Chapter 4 introduces Convolution Codes and their formal and graphical representation, Chap. 5 adds the decoding algorithms, such as Viterbi, SOVA, and BCJR. Puncturing and Pruning complete the chapter. In Chap. 6, we give an overview over sequential, tree-based decoding.
Trellis-Coded Modulation and Trellis Shaping follow in Chaps. 7 and 8, respectively. This finalizes the convolutional-coding-based part. Later, the block-coding-related part will also be terminated with coded modulation and shaping.
Chapter 9 provides the mathematical foundation for algebraic block codes which are finite fields, so-called Galois fields. They are not only the basis for block codes, but also for Cryptology and random number generation.
Reed-Solomon (RS) codes, as found in manifold applications directly (one may just think of the error correction for a CD or DVD) or as outer codes in a concatenation, are described in Chap. 10, introducing them as polynomial interpolation.
The treatment of RS decoding likewise begins with interpolation, this time an exponential one, to thereafter introduce the Berlekamp-Massey and Euclidean algorithms. Chapter 10 is concluded discussing error values. Bose-Chaudhuri-Hocqhenghem (BCH) codes follow as subfield subcodes of RS codes in Chap. 11.
“Modern” coding schemes are treated in Chap. 12, extending the codeword length as required from Information Theory to approach Capacity. Among the discussed modern coding schemes are Turbo, LDPC, and Polar codes.
Chapter 13 offers a short excursion to network-related coding. Error probabilities and coding bounds are then discussed in Chaps. 14 and 15, respectively.
As one of the links between block and convolutional codes, Chap. 16 offers construction possibilities for trellises of block codes, thereby allowing to use trellis-based maximum-likelihood (or MAP) decoders for block codes.
Multilevel Coded Modulation and Shaping by Shell Mapping are finalizing the treatment of this share in Chaps. 17 and 19, respectively, with an intermediate introduction of Lattices in Chap. 18 making use of multilevel code designs.
The book concludes with a collection of exercises and corresponding solutions.