Cryptography, Information Theory, and Error-Correction. Aiden A. Bruen

10.13 Subadditivity of the Function –x log x 10.14 Entropy and Cryptography 10.15 Problems 10.16 Solutions Chapter 11: Source Coding, Redundancy 11.1 Introduction, Source Extensions 11.2 Encodings, Kraft, McMillan 11.3 Block Coding, the Oracle, Yes–No Questions 11.4 Optimal Codes 11.5 Huffman Coding 11.6 Optimality of Huffman Coding 11.7 Data Compression, Redundancy 11.8 Problems 11.9 Solutions Chapter 12: Channels, Capacity, the Fundamental Theorem 12.1 Abstract Channels 12.2 More Specific Channels 12.3 New Channels from Old, Cascades 12.4 Input Probability, Channel Capacity 12.5 Capacity for General Binary Channels, Entropy 12.6 Hamming Distance 12.7 Improving Reliability of a Binary Symmetric Channel 12.8 Error Correction, Error Reduction, Good Redundancy 12.9 The Fundamental Theorem of Information Theory 12.10 Proving the Fundamental Theorem 12.11 Summary, the Big Picture 12.12 Postscript: The Capacity of the Binary Symmetric Channel 12.13 Problems 12.14 Solutions Chapter 13: Signals, Sampling, Coding Gain, Shannon's Information Capacity Theorem 13.1 Continuous Signals, Shannon's Sampling Theorem 13.2 The Band‐Limited Capacity Theorem 13.3 The Coding Gain Chapter 14: Ergodic and Markov Sources, Language Entropy 14.1 General and Stationary Sources 14.2 Ergodic Sources 14.3 Markov Chains and Markov Sources 14.4 Irreducible Markov Sources, Adjoint Source 14.5 Cascades and the Data Processing Theorem 14.6 The Redundancy of Languages 14.7 Problems 14.8 Solutions Chapter 15: Perfect Secrecy: The New Paradigm 15.1 Symmetric Key Cryptosystems 15.2 Perfect Secrecy and Equiprobable Keys 15.3 Perfect Secrecy and Latin Squares 15.4 The Abstract Approach to Perfect Secrecy 15.5 Cryptography, Information Theory, Shannon 15.6 Unique Message from Ciphertext, Unicity 15.7 Problems 15.8 Solutions Chapter 16: Shift Registers (LFSR) and Stream Ciphers 16.1 Vernam Cipher, Psuedo‐Random Key 16.2 Construction of Feedback Shift Registers 16.3 Periodicity 16.4 Maximal Periods, Pseudo‐Random Sequences 16.5 Determining the Output from 2m Bits 16.6 The Tap Polynomial and the Period 16.7 Short Linear Feedback Shift Registers and the Berlekamp‐Massey Algorithm 16.8 Problems 16.9 Solutions Chapter 17: Compression and Applications 17.1 Introduction, Applications 17.2 The Memory Hierarchy of a Computer 17.3 Memory Compression 17.4 Lempel–Ziv Coding 17.5 The WKdm Algorithms 17.6 Main Memory – to Compress or Not to Compress 17.7 Problems 17.8 Solutions

      12  Part III: Mainly Error‐Correction Chapter 18: Error‐Correction, Hadamard, and Bruen–Ott 18.1 General Ideas of Error Correction 18.2 Error Detection, Error Correction 18.3