Calculate the probability of error for the channel.

EE 8371 Homework 8 Electrical Engineering Department

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1. A binary erasure channel (BEC) is shown below

1−p

1−p

X Y

a

b

a

b

e

p

p

Assume the input density function Px D f˛1; ˛2g where ˛1 C ˛2 D 1.

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

(b.) Calculate the probability of error for the channel.

(c.) Calculate the conditional probabilities for the extended channel with X D fa; b; c; d; e; f; g; hg, with codewords Xc D f000; 001; 010; 011; 100; 101; 110; 111g

(d.) Calculate the channel capacity for the extended channel.