Unit 4607: Information Theory and Its Applications

1. Introduction to Information Theory

• Definition and scope of information theory
• Key concepts:
  • Entropy: measure of uncertainty
  • Information content and units (bits, nats)
  • Communication systems overview
• Importance of information theory in modern communication

2. Shannon's Information Theory

• Biography of Claude Shannon and historical context
• Mathematical formulation of entropy
• Concept of mutual information
• Channel capacity theorem
• Introduction to coding theory
• Significance of Shannon’s work and its impact

3. Source Coding Techniques

• Purpose of source coding: data compression
• Huffman coding:
  • Algorithm and tree construction
  • Optimal prefix codes
• Arithmetic coding:
  • Probability intervals
  • Advantages over Huffman coding
• Run-length encoding:
  • Basic principles
  • Use cases and limitations
• Comparison of source coding techniques

4. Channel Coding and Error Control

• Noisy communication channels and need for error control
• Error detection versus error correction
• Hamming codes:
  • Code construction
  • Error detection and correction capabilities
• Reed-Solomon codes:
  • Block codes and applications
  • Error correction in data storage and transmission
• Convolutional codes:
  • Encoding process
  • Viterbi decoding algorithm
• Practical examples of channel coding

5. Information Theory in Data Compression

• Lossless compression:
  • Role of entropy in minimum code length
  • Algorithms and efficiency
• Lossy compression:
  • Trade-offs between compression ratio and information loss
  • Examples (JPEG, MP3)
• Computational complexity considerations
• Evaluation metrics: compression ratio, fidelity, and speed

6. Coding Theory and Cryptography

• Overview of cryptography principles
• Role of coding theory in secure communication
• Encryption techniques leveraging coding theory
• Error correction and data integrity in cryptographic protocols
• Examples of secure coding schemes

7. Applications of Information Theory

• Telecommunications:
  • Optimizing data transmission
  • Network capacity planning
• Data storage:
  • Error correction in hard drives and SSDs
• Image and signal processing:
  • Compression and noise reduction
• Artificial intelligence:
  • Information measures in machine learning
• Emerging trends and future directions