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| (Note:Each chapter begins with an Introduction.) | |
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| Introduction | |
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| Background Review | |
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| Brief Review of Number Theory and Finite Fields | |
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| Discrete Fourier Transform over Finite Fields | |
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| Basefield Transforms over Finite Fields | |
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| Wavelets for Discrete-Time Signals | |
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| Previous Work on Finite-Field Wavelets | |
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| Some Basic Concepts of Error-Control Coding | |
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| Summary | |
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| Finite-Field Wavelet Basis Functions | |
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| Finite-Field Discrete-Time Basis | |
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| Construction of Mother Wavelet and Scaling Function | |
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| Summary | |
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| Double Circulant Wavelet Block Codes | |
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| Structure of Double Circulant Wavelet Coding | |
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| Maximum-Distance Separable Codes | |
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| Double Circulant Self-Dual Codes | |
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| Decoding Wavelet Codes | |
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| Summary | |
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| Theory of Paraunitary Filter Banks Over Fields of Characteristic Two | |
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| Background Review | |
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| Unitary Matrices OverGF(2 r) | |
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| PU Matrices in Fields of Characteristic Two | |
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| Factorization of PU Matrices inGF(2 r) | |
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| Summary | |
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| Arbitrary-Rate Wavelet Block Codes | |
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| Structure of Wavelet Coding | |
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| Rate 1/L Maximum-Distance Separable Codes | |
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| Arbitrary-Rate Wavelet Block Codes | |
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| Arbitrary-Rate Maximum-Distance Separable Codes | |
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| Decoding Arbitrary-Rate Wavelet Block Codes | |
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| Summary | |
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| Wavelet Convolutional Codes | |
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| Structure of Wavelet Convolutional Codes | |
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| Algebraic Properties of Wavelet Convolutional Encoders | |
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| Syndrome Generators and Dual Encoders | |
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| Self-Dual and Self-Orthogonal Convolutional Codes | |
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| Time-Varying Wavelet Convolutional Codes and Bipartite Trellises | |
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| Summary | |
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| Concluding Remarks | |
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| Contributions | |
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| Suggestions for Future Research | |
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| Proofs for Chapter 5 | |
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| Brief Review of Trellis Structures | |
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| Bibliography | |
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| Vita | |