Trellis Decoding of Block Codes

It is a great pleasure to be asked to write the Preface for this book on trellis decoding of error correcting block codes. The subject is extremely significant both theoretically and practically, and is very timely because of recent devel opments in the microelectronic implementation and range of application of error-control coding systems based on block codes. The authors have been notably active in signal processing and coding research and development for several years, and therefore very well placed to contribute to the state of the art on the subject of trellis decoding. In particular, the book represents a unique approach to many practical aspects of the topic. As the authors point out, there are two main classes of error control codes: block codes and convolutinal codes. Block codes came first historically and have a well-developed mathematical structure. Convolutional codes come later, and have developed heuristically, though a more formal treatment has emerged via recent developments in the theory of symbolic dynamics. Max imum likelihood (ML) decoding of powerful codes in both these classes is computationally complex in the general case; that is, ML decoding fails into the class of NP-hard computational problems. This arieses because the de coding complexity is an exponential function of key parameters of the code.

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1 Introduction.- 1.1 About The Book.- 1.2 Acknowledgments.- 2 Generalised Array Codes.- 2.1 Array Encoding Technique.- 2.2 Generalised Array Codes.- 2.3 Recursive Encoding Technique For Some Classes of Block Codes Based On Array Decomposition.- 2.4 Generalised Array Codes For Partial Response Channels.- 3 Trellis Structure of Block Codes.- 3.1 Introduction to the Problem.- 3.2 Fundamental Definitions.- 3.3 Trellis Representation Of Array Codes.- 3.4 Trellis Decoding of Generalised Array Codes.- 3.5 Trellis Decoding of Block Codes in PR Channels.- 4 Adaptive Encoding and Trellis Decoding Techniques.- 4.1 Adaptive Encoding/Decoding In Digital Communications.- 4.2 Adaptive Block Codes With Constant Dimension And Their Trellis Decoding.- 4.3 Adaptive Block Codes With Constant Code Length And Their Trellis Decoding.- 4.4 Nested Encoding And Trellis Decoding Technique.- 4.5 Application of Adaptive Encoding and Trellis Decoding In ARQ Systems.- 4.6 Adaptive Spectral Shaping Codes And Their Trellis Decoding.- 5 Reed-Solomon Codes and Their Trellis Decoding.- 5.1 Finite Fields and Reed-Solomon Codes.- 5.2 Array Decomposition Of Reed-Solomon Codes.- 5.3 Trellis Decoding of RS Codes.- 5.4 Shannon Product of Trellises.- 5.5 Syndrome Trellis Design for RS Codes.- 5.6 Coset trellises for RS Codes.- 5.7 Sub-Optimum Trellis Decoding of Reed-Solomon Codes.- 6 Application of Trellis Decoders: Multi-Functional Trellis Decoding of Block Codes.- 6.1 Elements of Multi-Functional Coding.- 6.2 Block-Coded Trellis Modulation.- 6.3 Synchronisation Protocols For Multi-Functional Trellis Decoding.- 6.4 Real-Time Channel Estimation In Multi-Functional Trellis Decoders.- References.- A Graphic Illustration of the Trellis Design Procedure for Array Codes.- B Graphic Illustration of the Trellis DesignProcedure for Block Codes.- C Graphic Simulation of Trellis Decoders.