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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 | |