hand writing assignment

CS 527/ECE 599 Error Correcting Codes
Assignment No. 1, Due: Friday January 17, 2020

1. In a transmission system a 0 is encodded as 00000 and 1 as 11111 and
these bits are sent through the binary symmetric channel where th

e

bit error probality is p. At the receiving end the decoding is done by
majority voting. What is the probability of error PE assuming p = 0.1?
When 0 is encoded as 0000000 and 1 as 1111111 and the decoding is
done again by majority voting, what is the value of PE for p = 0.1?

2. The alpha fetal protein test is meant to detect spina bifida in unborn
babies, a condition that affects 1 out of 1000 children who are born.
Let B be the event that the baby has spina bifida and Bc be the event
that it does not. The literature on the test indicates that 5% of the
time a healthy baby will cause a positive reaction. We will assume
that the test is positive 100% of the time spina bifida is present. Your
doctor has just told you that your alpha fetal protein test was positive.
What is the probability that your baby has spina bifida ?

3. A random number is selected uniformly from 0; 1; 2; 3; 4; 5; 6; 7
without replacement until 3 is chosen. Let X denote the number of
selection. Find the entropy H(X) in bits.

4. A box of 50 semiconductor chips includes 3 defective ones. 5 chips are
randomly chosen from this box. Let X denote the number of defective
chips. Find the entropy of H(X) in bits.

5. World Series. The world series is a seven game-series that terminates as
soon as either team wins four games. Let X be the random variable that
represents the outcome of a World Series between teams A and B; some
possible values of X are AAAA, ABABBB, and BABABAA. Let

Y

be the number of games played, which ranges from 4 to 7. Assuming
that A and B are equally matched and the games are independent,
calculate H(X) and H(Y ).

6. Erasure Channel. Consider the discrete memoryless channel as shown
in Figure 1. Assuming P (X = 0) = 2

3
and P (X = 1) =

1

3
, and p = 1

4
,

find

X

1

0 0

1
e

1 −

p

p
p

1 − p

Y

Figure 1: Erasure Channel

(a) H(X), H(Y )

(b) H(Y/X), H(X/Y )

(c) H(X, Y )

(d) I(X, Y )

7. A fair coin is flipped until the first head occurs. Let X denote the
number of flips required. Find H(X).