Fundamentals in Information Theory and Coding

Cover......Page 1
Front Matter......Page 2
 Cryptosystems: Role and Classification......Page 3
 Error Control Strategies......Page 5
  Definition and Classification......Page 7
 Representation of Binary Code Sequences......Page 8
 Information Rate, Decision Rate......Page 9
 Parameters of Detecting and Error Correcting Codes......Page 10
  Definitions and Classification......Page 15
  Block Ciphers......Page 17
 Role of an ITS......Page 24
 Shannon First Theorem (1948)......Page 32
 Information Entropy for a DMS (Shannon Entropy)......Page 33
 Information Rate, Decision Rate......Page 37
  Applications......Page 40
  Channel Capacity Using the Noise Matrix......Page 45
  Numeral Systems......Page 4
  Binary Codes Used in Data Transmission, Storage or Computing......Page 6
  Pulse Code Modulation (PCM)......Page 13
 Coding Efficiency: Compression Ratio......Page 28
 Measure of Discrete Information......Page 30
 Moments and Moment Rate......Page 36
  Mutual Information and Transinformation......Page 43
  Definition and Representation......Page 48
  Algebraic Encoding of Cyclic Codes......Page 49
  Lempel-Ziv Type Algorithms (LZ)......Page 50
  Arithmetic Coding......Page 55
  Syndrome Calculation and Error Detection......Page 57
  Delta Modulation (DM)......Page 59
  Delta-Sigma Modulation......Page 63
  The Millennium Watermark System [53]......Page 64
  Circuits for Cyclic Encoding and Decoding......Page 66
  Playfair Cipher......Page 11
 Maximum Likelihood Decoding (MLD)......Page 12
  Vigénère Cipher......Page 14
  Probabilities and Entropies in Discrete Channels......Page 38
  Principle of the Public Key Cryptography......Page 39
  Public Keys Ciphers......Page 42
  Introduction......Page 44
 Cyclic Codes......Page 47
  Finite and Homogeneous Markov Chains......Page 61
  Some Remarks......Page 69
  Backgrounds of Biomolecular Technologies......Page 70
  Elements of Biomolecular Computation (BMC)......Page 74
  Short History......Page 77
  Fire Codes......Page 84
  Linear Block Codes: Definition and Matrix Description......Page 16
  Error Syndrome......Page 19
  Perfect and almost Perfect Codes......Page 20
  Detection and Correction Capacity: Decoded BER......Page 21
  Relations between the Columns of H Matrix for Error Detection and Correction......Page 22
 References......Page 27
  Numeral Systems......Page 78
  Golay Code......Page 82
  Pulse Code Modulation (PCM)......Page 87
 Existence Theorem for Instantaneous and Uniquely Decodable Codes (Kraft and McMillan Inequalities)......Page 104
 Shannon First Theorem (1948)......Page 106
  Graphic Representation of Convolutional Codes......Page 112
  Code Distance and d∞......Page 116
  Decoding (Viterbi Algorithm, Threshold Decoding)......Page 118
  Interleaving......Page 132
  Concatenated Codes......Page 134
  Comparison and Applications of Digital Modulations......Page 138
 References......Page 140
 Line (baseband) Codes......Page 166
 References......Page 177
 Terminology......Page 23
 Model of an ITS......Page 25
 Memoryless Information Sources......Page 29
 Source Redundancy and Efficiency......Page 35
  Shannon Capacity......Page 52
 Memory Sources (Markov Sources)......Page 60
  Entropy of m-th Order Markov Source......Page 65
  Applications......Page 68
 References......Page 73
 What Is Coding and Why Is It Necessary?......Page 75
  Binary Codes Used in Data Transmission, Storage or Computing......Page 80
  Genetic Code......Page 98
 Coding Efficiency: Compression Ratio......Page 102
  Shannon-Fano Binary Coding......Page 107
  Huffman Algorithms......Page 110
  Run Length Coding (RLC)......Page 117
  Comma Coding......Page 122
  Dictionary Techniques [41]......Page 123
  Lempel-Ziv Type Algorithms (LZ)......Page 124
  Arithmetic Coding......Page 129
  Differential Pulse Code Modulation (DPCM)......Page 131
  Delta Modulation (DM)......Page 133
  Delta-Sigma Modulation......Page 137
 Short History of Cryptography......Page 142
 Terminology......Page 144
 Cryptanalytic Attacks and Algorithms Security......Page 146
  Definition and Classification......Page 148
  Caesar Cipher......Page 149
  Polybius Cipher......Page 151
  Playfair Cipher......Page 152
  Trithemius Cipher......Page 153
  Vigénère Cipher......Page 155
  Definitions and Classification......Page 156
  Block Ciphers......Page 158
  Stream Ciphers......Page 174
  Authentication with Symmetric Cryptography......Page 179
  Principle of the Public Key Cryptography......Page 180
  Public Keys Ciphers......Page 183
  Introduction......Page 185
  Short History......Page 188
  Watermarking Requirements......Page 189
  Basic Principles of Watermarking......Page 190
  Specific Attacks......Page 198
  Applications......Page 202
  The Millennium Watermark System [53]......Page 205
  Some Remarks......Page 210
  Introduction......Page 211
  Elements of Biomolecular Computation (BMC)......Page 215
  DNA Based Steganography and Cryptographic Algorithms......Page 218
 References......Page 225
 Shannon Second Theorem (Noisy Channels Coding Theorem)......Page 230
 Error Control Strategies......Page 234
 Representation of Binary Code Sequences......Page 237
 Parameters of Detecting and Error Correcting Codes......Page 239
 Maximum Likelihood Decoding (MLD)......Page 241
  Linear Block Codes: Definition and Matrix Description......Page 245
  Error Syndrome......Page 248
  Perfect and almost Perfect Codes......Page 249
  Detection and Correction Capacity: Decoded BER......Page 250
  Relations between the Columns of H Matrix for Error Detection and Correction......Page 251
  Standard Array and Syndrome Decoding......Page 253
  Comparison between Linear Error Detecting and Correcting Block Codes......Page 256
  Hamming Group Codes......Page 259
  Some Other Linear Block Codes......Page 274
 Cyclic Codes......Page 276
  Definition and Representation......Page 277
  Algebraic Encoding of Cyclic Codes......Page 278
  Syndrome Calculation and Error Detection......Page 286
  Algebraic Decoding of Cyclic Codes......Page 290
  Circuits for Cyclic Encoding and Decoding......Page 295
  Cyclic One Error Correcting Hamming Code......Page 307
  Golay Code......Page 311
  Fire Codes......Page 313
  Reed–Solomon Codes......Page 316
  Representation and Properties......Page 333
  Convolutional Codes Encoding......Page 335
  Graphic Representation of Convolutional Codes......Page 341
  Code Distance and d∞......Page 345
  Decoding (Viterbi Algorithm, Threshold Decoding)......Page 347
  Interleaving......Page 361
  Concatenated Codes......Page 363
  Definition and Encoding......Page 367
  Decoding......Page 369
 Line (baseband) Codes......Page 395
 References......Page 406
Back Matter......Page 409