Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000010113509 | QA76.9.D33 S44 2006 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
Shall we be destined to the days of eternity, on holy-days,as well as working days, to be shewing the RELICKS OF LEARNING, as monks do the relicks of their saints - without working one - one single miracle with them? Laurence Sterne, Tristram Shandy This book deals with information processing; so it is far from being a book on information theory (which would be built on description and estimation). The reader will be shown the horse, but not the saddle. At any rate, at the very beginning, there was a series of lectures on "Information theory, through the looking-glass of an algebraist", and, as years went on, a steady process of teaching and learning made the material evolve into the present form. There still remains an algebraic main theme: algorithms intertwining polynomial algebra and matrix algebra, in the shelter of signal theory. A solid knowledge of elementary arithmetic and Linear Algebra will be the key to a thorough understanding of all the algorithms working in the various bit-stream landscapes we shall encounter. This priority of algebra will be the thesis that we shall defend. More concretely: We shall treat, in ?ve chapters of increasing di?culty, ?ve sensibly di?erent subjects in Discrete Mathem- ics. The?rsttwochaptersondatacompaction(losslessdatacompression)and cryptography are on an undergraduate level - the most di?cult mathematical prerequisite will be a sound understanding of quotient rings, especially of- nite ?elds (mostly in characteristic 2).
Table of Contents
1 Data Compaction | p. 5 |
1.1 Entropy Coding | p. 5 |
1.1.1 Discrete Sources and Their Entropy | p. 5 |
1.1.2 Towards Huffman Coding | p. 10 |
1.1.3 Arithmetic Coding | p. 32 |
1.2 Universal Codes: The Example LZW | p. 43 |
1.2.1 LZW Coding | p. 43 |
1.2.2 The LZW Decoder | p. 45 |
2 Cryptography | p. 49 |
2.1 The Data Encryption Standard | p. 50 |
2.1.1 The DES Scheme | p. 50 |
2.1.2 The Cipher DES in Detail | p. 53 |
2.2 The Advanced Encryption Standard: The Cipher Rijndael | p. 60 |
2.2.1 Some Elementary Arithmetic | p. 60 |
2.2.2 Specification of Rijndael | p. 77 |
2.2.3 The Key Schedule | p. 86 |
2.2.4 Decryption with Rijndael | p. 92 |
2.3 The Public Key Paradigm and the Cryptosystem RSA | p. 93 |
2.3.1 Encryption and Decryption via Exponentiation | p. 93 |
2.3.2 The Cryptosystem RSA | p. 97 |
2.4 Digital Signatures | p. 101 |
2.4.1 Message Digests via SHA-1 | p. 101 |
2.4.2 DSA: Digital Signature Algorithm | p. 112 |
2.4.3 Auxiliary Algorithms for DSA | p. 116 |
2.4.4 The Signature Algorithm rDSA | p. 122 |
2.4.5 ECDSA - Elliptic Curve Digital Signatures | p. 125 |
3 Information Theory and Signal Theory: Sampling and Reconstruction | p. 171 |
3.1 The Discrete Fourier Transform | p. 172 |
3.1.1 Basic Properties | p. 172 |
3.1.2 The Fast Fourier Transform Algorithm | p. 183 |
3.2 Trigonometric Interpolation | p. 190 |
3.2.1 Trigonometric Polynomials | p. 191 |
3.2.2 Sampling and Reconstruction | p. 193 |
3.3 The Whittaker-Shannon Theorem | p. 198 |
3.3.1 Fourier Series | p. 198 |
3.3.2 The Whittaker-Shannon Theorem for Elementary Periodic Functions | p. 203 |
3.3.3 The (Continuous) Fourier Transform: A Sketch | p. 209 |
3.3.4 The Sampling Theorem | p. 214 |
4 Error Control Codes | p. 221 |
4.1 The Reed-Solomon Codes | p. 221 |
4.1.1 Preliminaries: Polynomial Codes | p. 221 |
4.1.2 Reed-Solomon Codes | p. 225 |
4.2 Convolutional Codes | p. 239 |
4.2.1 Encoding: Digital Filtering in Binary Arithmetic | p. 239 |
4.2.2 Decoding: The Viterbi Method | p. 253 |
5 Data Reduction: Lossy Compression | p. 267 |
5.1 DFT, Passband Filtering and Digital Filtering | p. 268 |
5.2 The Discrete Cosine Transform | p. 274 |
5.2.1 Functional Description of the DCT | p. 275 |
5.2.2 The 2D DCT | p. 293 |
5.2.3 The Karhunen-Loeve Transform and the DCT | p. 305 |
5.3 Filter Banks and Discrete Wavelet Transform | p. 314 |
5.3.1 Two Channel Filter Banks | p. 314 |
5.3.2 The Discrete Wavelet Transform | p. 372 |
References | p. 435 |
Index | p. 439 |