Electrical

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EE 8371 Homework 9 Electrical Engineering Department

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1. A modified binary erasure channel (MBEC) is shown below

r

r

X Y

a

b

a

b

e

p

p

q

q

Assume the input density function Px D f˛1; ˛2g where ˛1 C ˛2 D 1. Naturally, p C q C r D 1.

(a.) Calculate the error probabilities,

PŒX D a; Y ¤ a� D PŒY ¤ ajX D a�PŒX D a�;

PŒX D b; Y ¤ b� D PŒY ¤ bjX D b�PŒX D b�:

(b.) Calculate the channel capacity for X D fa; bg and Y D fa; e; bg with codewords Xc D f0; 1g.