FINITE FIELD WAVELET TRANSFORMS
Ouvrage 0-13-060020-2 : FINITE FIELD WAVELET TRANSFORMS
1. Introduction.
2. Background Review.
Introduction. Brief Review of Number Theory and Finite Fields. Discrete
Fourier Transform over Finite Fields. Basefield Transforms over Finite
Fields. Wavelets for Discrete-Time Signals. Previous Work on
Finite-Field Wavelets. Some Basic Concepts of Error-Control Coding.
Summary.
3. Finite-Field Wavelet Basis Functions.
Introduction. Finite-Field Discrete-Time Basis. Construction of Mother
Wavelet and Scaling Function. Summary.
4. Double Circulant Wavelet Block Codes.
Introduction. Structure of Double Circulant Wavelet Coding.
Maximum-Distance Separable Codes. Double Circulant Self-Dual Codes.
Decoding Wavelet Codes. Summary.
5. Theory of Paraunitary Filter Banks Over Fields of Characteristic Two.
Introduction. Background Review. Unitary Matrices Over GF( r). PU
Matrices in Fields of Characteristic Two. Factorization of PU Matrices
in GF( r). Summary.
6. Arbitrary-Rate Wavelet Block Codes.
Introduction. Structure of Wavelet Coding. Rate 1/L Maximum-Distance
Separable Codes. Arbitrary-Rate Wavelet Block Codes. Arbitrary-Rate
Maximum-Distance Separable Codes. Decoding Arbitrary-Rate Wavelet Block
Codes. Summary.
7. Wavelet Convolutional Codes.
Introduction. Structure of Wavelet Convolutional Codes. Algebraic
Properties of Wavelet Convolutional Encoders. Syndrome Generators and
Dual Encoders. Self-Dual and Self-Orthogonal Convolutional Codes.
Time-Varying Wavelet Convolutional Codes and Bipartite Trellises.
Summary. For graduate students, research engineers, practicing
professionals.
The primary focus of this work is to explore wavelets and filter banks
over finite fields and their intersection with error control coding and
data encryption. It develops the "theory of wavelet transforms over
finite fields" which provides a general wavelet decomposition of
sequences defined over finite fields - an approach that has a rich
history in signal processing for the representation of real-valued
signals, but which has been lacking in the finite field case. Along with
wavelet theory on finite fields, this work introduces the first
application of this theory to error correcting codes and data security.
It also introduces a finite-field wavelet based public key encryption
technique.
Features and Benefits
New mathematical tool (wavelet transforms over finite fields), can be
used in signal processing and communications.
Novel error control coding methods based on wavelets, introduces the
first application of the finite-field wavelets to error control coding.
Novel security coding methods based on wavelets, introduces the first
application of the finite-field wavelets to data encryption.
Impact on basic science, brings together researchers from the areas of
applied discrete mathematics, signal processing and communications
research and provides new connections and new interpretations.
Impact on technology and products, provides students with orientations
toward practical applications, reducing decoding complexity, and
satisfying low computing requirements.
Unique treatment of coding and security, exploits finite-field wavelet
techniques for coding and security and provides a state-of-the-art
knowledge about the new treatment of coding and security.
Auteur : FEKRI
Editeur : PRENTICE HALL
Nombre de pages : 260
Date de publication : 10 2005
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