Entropy and Data Compression: Huffman Coding Techniques

This lecture covers the concepts of entropy and data compression, focusing on Huffman coding techniques. It begins with a review of average codeword lengths and the relationship between entropy and coding efficiency. The instructor explains the main theorem regarding the average codeword length of a D-ary Shannon-Fano code, establishing bounds related to entropy. The lecture then delves into the Huffman algorithm, illustrating how it optimally compresses data by merging the least likely symbols. The discussion includes the importance of conditional entropy and its implications for coding sequences of symbols. The instructor emphasizes the significance of understanding joint entropy and the behavior of independent and identically distributed (IID) sources. The lecture concludes with practical examples and exercises to reinforce the concepts of conditional probability and expectation, highlighting their relevance in real-world applications such as text and audio compression.