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Information Theory, Coding and Cryptography

Book Description

Information Theory, Coding & Cryptography has been designed as a comprehensive text for the students of engineering discussing Source Encoding, Error Control Codes & Cryptography. The book contains the recent developments of coded modulation, trellises for codes, turbo coding for reliable data and interleaving. The text balances the mathematical rigor with exhaustive amount of solved, unsolved questions along with a database of MCQ's.

Table of Contents

  1. Cover
  2. Title Page
  3. Contents
  4. Foreword
  5. Preface
  6. Part A: Information Theory and Source CodinG
    1. Chapter 1: Probability, Random Processes, and Noise
      1. 1.1 Introduction
      2. 1.2 Fundamentals of Probability
        1. 1.2.1 Algebra of Probability
        2. 1.2.2 Axioms of Probability
        3. 1.2.3 Elementary Theorems on Probability
        4. 1.2.4 Conditional Probability
        5. 1.2.5 Independent Events
        6. 1.2.6 Total Probability
      3. 1.3 Random Variables and Its Characteristics
        1. 1.3.1 Discrete Random Variable and Probability Mass Function
        2. 1.3.2 Cumulative Distribution Function
        3. 1.3.3 Distribution Function for Discrete Random Variable
        4. 1.3.4 Continuous Random Variable and Probability Density Function
      4. 1.4 Statistical Averages
      5. 1.5 Frequently Used Probability Distributions
        1. 1.5.1 Binomial Distribution
        2. 1.5.2 Poisson Distribution
        3. 1.5.3 Gaussian Distribution
      6. 1.6 Random Processes
      7. 1.7 Noise
        1. 1.7.1 Sources of Noise
        2. 1.7.2 Thermal Noise
        3. 1.7.3 Shot Noise
        4. 1.7.4 Partition Noise
        5. 1.7.5 Flicker Noise or 1/f Noise
      8. 1.8 Solved Problems
      9. Multiple Choice Questions
      10. Review Questions
    2. Chapter 2: Information Theory
      1. 2.1 Introduction
      2. 2.2 Measure of Information
      3. 2.3 Entropy
      4. 2.4 Information Rate
      5. 2.5 Channel Model
        1. 2.5.1 Discrete Memoryless Channel
        2. 2.5.2 Special Channels
      6. 2.6 Joint Entropy and Conditional Entropy
      7. 2.7 Mutual Information
      8. 2.8 Channel Capacity
        1. 2.8.1 Special Channels
      9. 2.9 Shannon’s Theorem
      10. 2.10 Continuous Channel
        1. 2.10.1 Differential Entropy
        2. 2.10.2 Additive White Gaussian Noise Channel
        3. 2.10.3 Shannon–Hartley Law
      11. 2.11 Solved Problems
      12. Multiple Choice Questions
      13. Review Questions
    3. Chapter 3: Source Codes
      1. 3.1 Introduction
      2. 3.2 Coding Parameters
      3. 3.3 Source Coding Theorem
      4. 3.4 Classification of Codes
      5. 3.5 Kraft Inequality
      6. 3.6 Image Compression
      7. 3.6.1 Image Formats, Containers, and Compression Standards
      8. 3.7 Speech and Audio Coding
      9. 3.8 Shannon–Fano Coding
      10. 3.9 Huffman Coding
      11. 3.10 Arithmetic Coding
      12. 3.11 Lempel–Ziv–Welch Coding
      13. 3.12 Run-length Encoding
      14. 3.13 MPEG Audio and Video Coding Standards
      15. 3.14 Psychoacoustic Model of Human Hearing
        1. 3.14.1 The Masking Phenomenon
        2. 3.14.2 Temporal Masking
        3. 3.14.3 Perceptual Coding in MPEG Audio
      16. 3.15 Dolby
      17. 3.16 Linear Predictive Coding Model
      18. 3.17 Solved Problems
      19. Multiple Choice Questions
      20. Review Questions
  7. Part B: Error Control Coding
    1. Chapter 4: Coding Theory
      1. 4.1 Introduction
      2. 4.2 Types of Codes
      3. 4.2.1 Code Rate
      4. 4.3 Types of Errors
      5. 4.4 Error Control Strategies
        1. 4.4.1 Throughput Efficiency of ARQ
      6. 4.5 Mathematical Fundamentals
        1. 4.5.1 Modular Arithmetic
        2. 4.5.2 Sets
        3. 4.5.3 Groups
        4. 4.5.4 Fields
        5. 4.5.5 Arithmetic of Binary Field
        6. 4.5.6 Roots of Equations
        7. 4.5.7 Galois Field
      7. 4.6 Vector Spaces
        1. 4.6.1 Subspace
        2. 4.6.2 Linear Combination
        3. 4.6.3 Basis (or Base)
        4. 4.6.4 Dimension
        5. 4.6.5 Orthogonality
        6. 4.6.6 Dual Space
      8. 4.7 Matrices
        1. 4.7.1 Row Space
      9. 4.8 Solved Problems
      10. Multiple Choice Questions
      11. Review Questions
    2. Chapter 5: Linear Block Codes
      1. 5.1 Introduction
      2. 5.2 Generator Matrices
      3. 5.3 Parity-check Matrices
        1. 5.3.1 Dual Code
      4. 5.4 Error Syndrome
        1. 5.4.1 Undetectable Error Pattern
      5. 5.5 Error Detection
      6. 5.6 Minimum Distance
      7. 5.7 Error-detecting Capability
      8. 5.8 Error-correcting Capability
      9. 5.9 Standard Array and Syndrome Decoding
        1. 5.9.1 Coset and Coset Leader
      10. 5.10 Probability of Undetected Errors Over a BSC
      11. 5.11 Hamming Code
      12. 5.12 Solved Problems
      13. Multiple Choice Questions
      14. Review Questions
    3. Chapter 6: Cyclic Codes
      1. 6.1 Introduction
      2. 6.2 Generation
        1. 6.2.1 Generation and Parity-check Matrices
        2. 6.2.2 Realization of Cyclic Code
      3. 6.3 Syndrome Computation and Error Detection
      4. 6.4 Decoding
      5. 6.5 Cyclic Hamming Code
      6. 6.6 Shortened Cyclic Code
      7. 6.7 Golay Code
      8. 6.8 Error-trapping Decoding
        1. 6.8.1 Improved Error-trapping
      9. 6.9 Majority Logic Decoding
      10. 6.10 Cyclic Redundancy Check
      11. 6.11 Solved Problems
      12. Multiple Choice Questions
      13. Review Questions
    4. Chapter 7: BCH Codes
      1. 7.1 Introduction
      2. 7.2 Primitive Elements
      3. 7.3 Minimal Polynomials
      4. 7.4 Generator Polynomials
      5. 7.5 Decoding of BCH Codes
      6. 7.6 Implementation of Galois Field
      7. 7.7 Implementation of Error Correction
        1. 7.7.1 Syndrome Computation
        2. 7.7.2 Computation of Error Location Polynomial
      8. 7.8 Nonbinary BCH Codes
        1. 7.8.1 Reed–Solomon Code
      9. 7.9 Weight Distribution
      10. 7.10 Solved Problems
      11. Multiple Choice Questions
      12. Review Questions
    5. Chapter 8: Convolution Codes
      1. 8.1 Introduction
      2. 8.2 Tree and Trellis Codes
      3. 8.3 Encoding
      4. 8.4 Properties
        1. 8.4.1 Structural Properties
        2. 8.4.2 Distance Properties
      5. 8.5 Decoding
        1. 8.5.1 Threshold Decoding
        2. 8.5.2 Sequential Decoding
        3. 8.5.3 Viterbi Decoding
      6. 8.6 Construction
      7. 8.7 Implementation and Modification
      8. 8.8 Applications
      9. 8.9 Turbo Coding and Decoding
      10. 8.10 Interleaving Techniques: Block and Convolution
      11. 8.11 Coding and Interleaving Applied to CD Digital Audio System
        1. 8.11.1 CIRC Encoding and Decoding
        2. 8.11.2 Interpolation and Muting
      12. 8.12 Solved Problems
      13. Multiple Choice Questions
      14. Review Questions
  8. Part C: Cryptography
    1. Chapter 9: Cryptography
      1. 9.1 Introduction
      2. 9.2 Plain Text, Cipher Text, and Key
      3. 9.3 Substitution and Transposition
      4. 9.4 Encryption and Decryption
      5. 9.5 Symmetric-key Cryptography
        1. 9.5.1 Stream Ciphers and Block Ciphers
      6. 9.6 Data Encryption Standard
        1. 9.6.1 Basic Principle
        2. 9.6.2 Initial Permutation
        3. 9.6.3 Details of Single Round
        4. 9.6.4 Inverse Initial Permutation
        5. 9.6.5 DES Decryption
        6. 9.6.6 Strength of DES
      7. 9.7 Advance Versions of DES
        1. 9.7.1 Double DES
        2. 9.7.2 Triple DES
      8. 9.8 Asymmetric-key Cryptography
        1. 9.8.1 Public and Private Key
      9. 9.9 RSA Algorithm
        1. 9.9.1 Example of RSA
        2. 9.9.2 Strength of RSA
      10. 9.10 Symmetric versus Asymmetric-key Cryptography
      11. 9.11 Diffie–Hellman Key Exchange
      12. 9.11.1 The Algorithm
      13. 9.12 Steganography
      14. 9.13 Quantum Cryptography
      15. 9.14 Solved Problems
      16. Multiple Choice Questions
      17. Review Questions
  9. Appendix A: Some Related Mathematics
    1. A.1 Fermat’s Little Theorem
    2. A.2 Chinese Remainder Theorem
    3. A.3 Prime Number Generation
      1. A.3.1 Sieve of Eratosthenes
  10. Notes
  11. Bibliography
  12. Copyright
  13. Back Cover