Monthly Archives: July 2010

Walking Downhill

The problem asks you to show that . If , then the solution is quite easy. Set the gradient equal to zero and solve the system of equations for . Since the function is convex, this is the minimum point, and … Continue reading

Posted in Information Theory, Papers | 1 Comment

4 Prisoners

The end of the 100 Prisoners post asked if there is a way to show that there does not exist a strategy that meets the coupon collector lower bound for release when there are prisoners. Let’s first establish strategies for … Continue reading

Posted in Probability, Puzzle | Leave a comment

Shannon Meets Shannon

He’s met almost everyone else: Wiener, Bode, Bellman, Carnot, Tesla, Marconi, and of course, Shortz. Bad jokes aside, in an attempt to understand the inverse water filling solution from rate-distortion theory better, I put together some rough notes attempting to connect it and the sampling … Continue reading

Posted in Information Theory, Signal Processing | 1 Comment