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

### 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

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 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 |