Algorithmic Information Theory: Mathematics of Digital Information Processing - ISBN:3540332189

Algorithmic Information Theory: Mathematics of Digital Information Processing

Date: 06 May 2011, 20:08

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This book treats the Mathematics of many important areas in digital information processing.
It covers, in a unified presentation, five topics: Data Compression, Cryptography, Sampling (Signal Theory), Error Control Codes, Data Reduction. The thematic choices are practice-oriented. So, the important final part of the book deals with the Discrete Cosine Transform and the Discrete Wavelet Transform, acting in image compression. The presentation is dense, the examples and numerous exercises are concrete. The pedagogic architecture follows increasing mathematical complexity. A read-and-learn book on Concrete Mathematics, for teachers, students and practitioners in Electronic Engineering, Computer Science and Mathematics.
Contents
1 Data Compaction
1.1 Entropy Coding
1.1.1 Discrete Sources and Their Entropy
1.1.2 Towards Huffman Coding
1.1.3 Arithmetic Coding
1.2 Universal Codes: The Example LZW
1.2.1 LZW Coding
1.2.2 The LZW Decoder
2 Cryptography
2.1 The Data Encryption Standard
2.1.1 The DES Scheme
2.1.2 The Cipher DES in Detail
2.2 The Advanced Encryption Standard: The Cipher Rijndael
2.2.1 Some Elementary Arithmetic
2.2.2 Specification of Rijndael
2.2.3 The Key Schedule
2.2.4 Decryption with Rijndael
2.3 The Public Key Paradigm and the Cryptosystem RSA
2.3.1 Encryption and Decryption via Exponentiation
2.3.2 The Cryptosystem RSA
2.4 Digital Signatures
2.4.1 Message Digests via SHA-1
2.4.2 DSA: Digital Signature Algorithm
2.4.3 Auxiliary Algorithms for DSA
2.4.4 The Signature Algorithm rDSA
2.4.5 ECDSA - Elliptic Curve Digital Signatures
3 Information Theory and Signal Theory: Sampling and Reconstruction
3.1 The Discrete Fourier Transform
3.1.1 Basic Properties
3.1.2 The Fast Fourier Transform Algorithm
3.2 Trigonometric Interpolation
3.2.1 Trigonometric Polynomials
3.2.2 Sampling and Reconstruction
3.3 The Whittaker-Shannon Theorem
3.3.1 Fourier Series
3.3.2 The Whittaker-Shannon Theorem for Elementary Periodic Functions
3.3.3 The (Continuous) Fourier Transform: A Sketch
3.3.4 The Sampling Theorem
4 Error Control Codes
4.1 The Reed-Solomon Codes
4.1.1 Preliminaries: Polynomial Codes
4.1.2 Reed-Solomon Codes
4.2 Convolutional Codes
4.2.1 Encoding: Digital Filtering in Binary Arithmetic
4.2.2 Decoding: The Viterbi Method
5 Data Reduction: Lossy Compression
5.1 DFT, Passband Filtering and Digital Filtering
5.2 The Discrete Cosine Transform
5.2.1 Functional Description of the DCT
5.2.2 The 2D DCT
5.2.3 The Karhunen-Lo`eve Transform and the DCT
5.3 Filter Banks and Discrete Wavelet Transform
5.3.1 Two Channel Filter Banks
5.3.2 The Discrete Wavelet Transform
References
Index
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