Digital Signal Processing

Digital Signal Processing

Applications to Communications and Algebraic Coding Theories

First published on February 28, 1989

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  • Author: Salvatore Morgera
  • eBook ISBN: 9780323158930

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Digital Signal Processing: Applications to Communications and Algebraic Coding Theories discusses the design of computationally efficient digital signal processing algorithms over finite fields and the relation of these algorithms to algebraic error-correcting codes. The book provides chapters that cover such topics as signal processing techniques employed for modeling, synthesis, and analysis; systems of bilinear forms; efficient finite field algorithms; the design and study of long length cyclic convolutions and some preliminary results on their relation to linear codes; the study of the algebraic structure of the class of linear codes obtained from bilinear cyclic and aperiodic convolution algorithms over the finite field of interest; and the concept of a generalized hybrid Automatic- Repeat-Request (ARQ) scheme for adaptive error control in digital communication systems. Engineers, mathematicians, and computer scientists will find the text invaluable.

Table of Contents

  • Preface


    1 Overview and Perspective

    1.1 Introduction

    1.2 Breadth and Depth

    1.3 References

    2 Systems of Bilinear Forms

    2.1 The Program Model

    2.2 Multiplicative Complexity

    2.3 Dual of a Bilinear Form

    2.4 A Particular Bilinear Form

    2.5 References

    3 Efficient Finite Field Algorithms

    3.1 Cyclic Convolution

    3.1.1 Algorithm Development

    3.1.2 Algorithm Steps

    3.1.3 Length p — 1 Algorithms Over a Field of Constants GF(p)

    3.1.4 Length N Algorithms Over a Field of Constants GF(p) When (N,p) = 1

    3.1.5 Multiplicative Complexity

    3.1.6 Additive Complexity

    3.2 Aperiodic Convolution

    3.2.1 The Toom-Cook Algorithm

    3.2.2 Embedding of Aperiodic Convolution: Higher-Dimensional Approaches

    3.2.3 Aperiodic Convolution with Wraparound

    3.3 References

    3.4 Appendix A

    3.5 Appendix B

    3.6 Appendix C

    4 Multidimensional Methods

    4.1 Long Length Cyclic Convolution

    4.1.1 Mutual Prime Factor Versus Direct Designs

    4.1.2 Some Specific Results Pertinent to Long Length Design

    4.2 Multiplicative Complexity

    4.3 A Distance Bound

    4.4 References

    4.5 Appendix A

    4.6 Appendix B

    5 A New Class of Linear Codes

    5.1 Multidimensional Algorithms and Codes

    5.2 CRT Algorithms and Codes

    5.2.1 CRT-Based Convolution Algorithms over GF(2) and the Related Codes

    5.2.2 CRT-Based Convolution Algorithms over GF(3) and the Related Codes

    5.2.3 A Shift Register-Based Encoding Procedure

    5.3 Error Detection

    5.3.1 Burst Error Detection Capability

    5.4 Error Correction

    5.4.1 Experimental Results

    5.4.2 Code Family Encoding/Decoding Relationships

    5.5 Discussion

    5.6 References

    5.7 Appendix A

    5.8 Appendix B

    6 A New Error Control Scheme

    6.1 ARQ Schemes

    6.2 Hybrid ARQ Schemes

    6.3 Generalized Type-II Hybrid ARQ Schemes

    6.4 A Brief Review of the KM Codes

    6.5 A GH-ARQ Scheme Based on KM Codes

    6.6 GH-ARQ Error Detection

    6.7 Reliability and Throughput

    6.8 Soft-Decision Decoding

    6.8.1 Background

    6.8.2 System Performance

    6.8.3 Performance Comparisons

    6.8.4 Soft-Decision GH-ARQ Code Alternatives

    6.9 References

    6.10 Appendix A

    6.11 Appendix B

    6.12 Appendix C

Product details

  • No. of pages: 254
  • Language: English
  • Copyright: © Academic Press 1989
  • Published: February 28, 1989
  • Imprint: Academic Press
  • eBook ISBN: 9780323158930

About the Author

Salvatore Morgera

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