Theory and Coding EPFL Winter Semester 2009 / 2010
نویسنده
چکیده
Problem 2 (Parallel Channels and Choice of channels) (a) Find the capacity C of the union of two channels (X1, p1(y1|x1),Y1) and (X2, p2(y2|x2),Y2), where at each time, one can send a symbol over channel 1 or channel 2 but not both. Assume that the output alphabets are distinct and do not intersect. Show that 2 = 21 + 22 . Thus 2 is the effective alphabet size of a channel with capacity C. (b) Consider two discrete memoryless channels (X1, p(y1|x1),Y1) and (X2, p(y2|x2),Y2) with capacities C1 and C2 respectively. A new channel (X1 ×X2, p(y1|x1)× p(y2|x2),Y1 × Y2) is formed in which x1 ∈ X1 and x2 ∈ X2 are sent simultaneously, resulting in y1, y2. Find the capacity of this channel. (c) Find the capacity of the following channel.
منابع مشابه
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• You are allowed to use 1 sheet of paper for reference. No mobile phones or calculators are allowed in the exam. • You can attempt the problems in any order as long as it is clear which problem is being attempted and which solution to the problem you want us to grade. • If you are stuck in any part of a problem do not dwell on it, try to move on and attempt it later. • Please solve every probl...
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