CN-GATEBOOK

Question

I think for (C), it should be The probability of "not detecting" a burst error of size 9 is $\frac{1}{2^7}$

And for (D), the probability of detecting burst error of size 15 should be  $1-\frac{1}{2^8}$

 

Correct me if I am wrong.

Answer 1

IF L is length of burst error  &  polynomial generator has highest degree as r.

1.All burst errors with L ≤ r will be detected.

2.All burst errors with L = r + 1 will be  detected with probability 1 – (1/2)^r–1.

3.All burst errors with L > r + 1 will be detected with probability 1 – (1/2)^r.

Now , as r = 8 here so it will be able to detect burst error of size 6 and it will dtect single bit error so option a and b are true

Now probabiltiy of detecting burst error of size 9 = 1-(1/2)^8 -------[by second rule as L = r+1, L=9 and r = 8]

and probabiltiy of detecting burst error of size 15 = 1-(1/2)^15-----[by third rule as L>r+1, L=15 and r = 8]

so both option c and option d are false 

Comments

$r$ = 8,

probability of detecting burst error of size 15  = $1 - (\frac{1}{2})^r = 1 - (\frac{1}{2})^8 $