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Cover image for Algorithmic information theory : mathematics of digital information processing
Title:
Algorithmic information theory : mathematics of digital information processing
Personal Author:
Series:
Signals and communication technology ; 1860-4862
Publication Information:
London : Springer, 2006
ISBN:
9783540332183

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30000010113509 QA76.9.D33 S44 2006 Open Access Book Book
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Summary

Summary

Algorithmic Information Theory treats the mathematics of many important areas in digital information processing. It has been written as a read-and-learn book on concrete mathematics, for teachers, students and practitioners in electronic engineering, computer science and mathematics. The presentation is dense, and the examples and exercises are numerous. It is based on lectures on information technology (Data Compaction, Cryptography, Polynomial Coding) for engineers.


Table of Contents

1 Data Compactionp. 5
1.1 Entropy Codingp. 5
1.1.1 Discrete Sources and Their Entropyp. 5
1.1.2 Towards Huffman Codingp. 10
1.1.3 Arithmetic Codingp. 32
1.2 Universal Codes: The Example LZWp. 43
1.2.1 LZW Codingp. 43
1.2.2 The LZW Decoderp. 45
2 Cryptographyp. 49
2.1 The Data Encryption Standardp. 50
2.1.1 The DES Schemep. 50
2.1.2 The Cipher DES in Detailp. 53
2.2 The Advanced Encryption Standard: The Cipher Rijndaelp. 60
2.2.1 Some Elementary Arithmeticp. 60
2.2.2 Specification of Rijndaelp. 77
2.2.3 The Key Schedulep. 86
2.2.4 Decryption with Rijndaelp. 92
2.3 The Public Key Paradigm and the Cryptosystem RSAp. 93
2.3.1 Encryption and Decryption via Exponentiationp. 93
2.3.2 The Cryptosystem RSAp. 97
2.4 Digital Signaturesp. 101
2.4.1 Message Digests via SHA-1p. 101
2.4.2 DSA: Digital Signature Algorithmp. 112
2.4.3 Auxiliary Algorithms for DSAp. 116
2.4.4 The Signature Algorithm rDSAp. 122
2.4.5 ECDSA - Elliptic Curve Digital Signaturesp. 125
3 Information Theory and Signal Theory: Sampling and Reconstructionp. 171
3.1 The Discrete Fourier Transformp. 172
3.1.1 Basic Propertiesp. 172
3.1.2 The Fast Fourier Transform Algorithmp. 183
3.2 Trigonometric Interpolationp. 190
3.2.1 Trigonometric Polynomialsp. 191
3.2.2 Sampling and Reconstructionp. 193
3.3 The Whittaker-Shannon Theoremp. 198
3.3.1 Fourier Seriesp. 198
3.3.2 The Whittaker-Shannon Theorem for Elementary Periodic Functionsp. 203
3.3.3 The (Continuous) Fourier Transform: A Sketchp. 209
3.3.4 The Sampling Theoremp. 214
4 Error Control Codesp. 221
4.1 The Reed-Solomon Codesp. 221
4.1.1 Preliminaries: Polynomial Codesp. 221
4.1.2 Reed-Solomon Codesp. 225
4.2 Convolutional Codesp. 239
4.2.1 Encoding: Digital Filtering in Binary Arithmeticp. 239
4.2.2 Decoding: The Viterbi Methodp. 253
5 Data Reduction: Lossy Compressionp. 267
5.1 DFT, Passband Filtering and Digital Filteringp. 268
5.2 The Discrete Cosine Transformp. 274
5.2.1 Functional Description of the DCTp. 275
5.2.2 The 2D DCTp. 293
5.2.3 The Karhunen-Loeve Transform and the DCTp. 305
5.3 Filter Banks and Discrete Wavelet Transformp. 314
5.3.1 Two Channel Filter Banksp. 314
5.3.2 The Discrete Wavelet Transformp. 372
Referencesp. 435
Indexp. 439
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