Shannon's Capacity as a Convex Optimization Problem | Convex Optimization Application # 11
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The Capacity is an achievable upper-bound of date rates on communication channels.
In this one, we formulate the famous capacity as a convex optimization and discuss the primal/dual formulations. We also solve these problems using the famous CVX toolbox on MATLAB. Formulations are highly inspired by [1]. The outline is as follows:
⏲⏲Outline⏲⏲
00:00 Introduction
02:42 The binary symmetric channel (BSC)
05:11 Mutual Information
08:23 Capacity as a convex optimization problem
15:35 Installing CVX
16:30 Primal Capacity Problem
19:38 Interpretation of the Primal solution in BSC (1-H(p))
24:40 Dual problem
38:18 Dual Capacity on MATLAB
42:35 ideal instances of the problem
44:11 Outro
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📚📚References📚📚
[1] Stephen P. Boyd, and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.
📹📹 Video 📹📹
NB: Lecture available in 4K
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