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This lecture discusses the achievable rate and capacity in communication systems, focusing on the relationship between power, bandwidth, and capacity. It covers the impact of increasing power and bandwidth on capacity, as well as the trade-offs involved. The lecture also explores the concept of degrees of freedom and how they affect the overall system performance, emphasizing the importance of power efficiency and spectral efficiency. Additionally, it delves into topics such as signal-to-noise ratio, fading channels, and error probabilities in communication systems.