# asynchronous communications-Error detection

#### dhammikai

Joined Sep 12, 2009
10

Assume an asynchronous communications protocol with 1 start bit, 2 stop bits, 1 parity bit, and 7 data bits. Assume that the start and stop bits are never in error, but for the remaining bits the Bit Error Probability = 0.05 (bit errors are independent).
Then need to be find the probability that a received word is error-free? and
Need to find highest possible probability of bit error if the probability that a received word is error-free must be no less than 0.80?

Last edited:

#### dhammikai

Joined Sep 12, 2009
10
My email [has been removed by moderator]

Last edited by a moderator:

#### Papabravo

Joined Feb 24, 2006
17,025
So what are your initial thoughts on how we might approach the solution?
An 8 bit number can have no errors, or any number of errors from 1 to 8. It is just like coin flips with p(Heads) = 0.95 and p(Tails)=.05 -- Isn't it?

#### dhammikai

Joined Sep 12, 2009
10
Hi thanks for the reply and commnets...but I am in stuck with my problem, but I found one PDF file (Attached here with) In the attachment question 07 is same as the my one but couldn't understand how it is solved.....

#### Attachments

• 83.2 KB Views: 91

#### Papabravo

Joined Feb 24, 2006
17,025
Hi thanks for the reply and commnets...but I am in stuck with my problem, but I found one PDF file (Attached here with) In the attachment question 07 is same as the my one but couldn't understand how it is solved.....
Do you know what "independent identically distributed" means, and why it is important in this context? If not, then you need to go back and review this concept. Now a simpler problem. You have a "fair" coin with p(Heads) = p(Tails) = 0.5. If each flip is independent and the distribution remains the same for each flip; what is the probability of getting two heads out of two flips? Isn't your problem the same except for the probabilities (an unfair coin) and the number of trials?

Last edited:

#### dhammikai

Joined Sep 12, 2009
10
This asynchronous communication has a 1 start bit, 2 stop bits, 1 parity bit, and 7 data bits.
here that the start and stop bits are never in error.
We needs to concern about remaining bits the Bit Error Probability = 0.05 (bit errors are independent).[The remaining 8 bits has 0.05 (5%) error probability. It means bit has 5% error probability (it also means 95% is error free probability)]
The answer should be " What is the probability that a received word is error-free?" is 95%, isn't it? I need Ur comments again..

#### Papabravo

Joined Feb 24, 2006
17,025
No it is not, and please don't restate the problem, I got it the first time and it creates a bad impression when you do that. Each bit may be regarded as an independent trial, aka flip of a coin. Each trial has p(Error) = 0.05 and p(No Error) = 0.95. The p(NoError) over 8 bits is most certainly not 0.95 Go back and review the material on repeated trials or Bernouli trials. If that does not make the light bulb go on, then take a coin and flip it 8 times. Did you get eight heads in a row? No then do it another 8 times, UNTIL you get eight heads in a row. How many times did it take you before you got eight heads in a row. Now assume the coin is unfair such that p(Heads) is 0.95 and the p(Tails) is 0.05 and ask what is the p(8 heads in a row), and you will have your answer.

Last edited: