Entropy and Compression I

This lecture covers the theory of entropy, including the upper bound demonstration and two quizzes. It explores properties of entropy, such as the relationship between probability and entropy, the concept of total order, and concavity. The lecture delves into compression without loss, explaining how data compression reduces storage space and transmission time by eliminating redundancy. It introduces algorithms like Shannon-Fano, demonstrating how to assign bit sequences to letters based on the number of questions needed to guess them. The lecture concludes by discussing the performance of the Shannon-Fano algorithm in reducing the number of bits required to represent a message, showcasing its efficiency in data compression.