Digital Signal Processing
Applications to Communications and Algebraic Coding Theories
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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
Acknowledgments
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