13-08-2012, 10:50 AM
09EC352: Information Theory and Coding
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1. For the discrete channel shown below, if all the indicated paths have a
probability of 0.5, write the probability transition matrix. Also nd the
mutual information, capacity and the input distribution that achieves ca-
pacity.
X Y
2. For the discrete channel shown below, write the probability transition
matrix and nd the mutual information.
X Y
1−p
p
(a) How much information is transferred from the input to the output if
p = 0:1 and the input distribution is f0:4; 0:6g?
(b) Find the capacity of the channel. (Hint: dierentiate I(X; Y ) w.r.t
p1, where p1 = PfX = x1g and equate to 0.)
3. A discrete channel is described by Y = X + Z, where the input X takes
the values 0 and 1 with probabilities p and 1