Source Coding Theorems: Entropy and Source Models

This lecture focuses on advanced concepts in source coding, particularly the source coding theorem and its implications for entropy. The instructor begins by summarizing previous results, emphasizing that conditioning reduces entropy. The discussion then shifts to the chain rule of entropy, which allows for the analysis of multiple random variables. The instructor explains how to compress long sequences of random variables, highlighting the importance of understanding the average number of bits used per symbol. Various source models are introduced, including IID sources and Markov processes, with specific examples like coin-flip and sunny-rainy sources. The lecture also covers the concept of regular sources and stationary sources, detailing their statistical properties and how they relate to entropy rates. The instructor concludes by discussing the implications of these concepts for coding and compression, emphasizing the significance of entropy as a measure of information and its applications in various fields.