Digital Signal Processing

PrefaceAcknowledgments1 Overview and Perspective 1.1 Introduction 1.2 Breadth and Depth 1.3 References2 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 References3 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 C4 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 B5 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 B6 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