22 Jan 10 7:39
I am trying to calculate the probability of an undetected error in a data-frame that is
sent through an embedded wireless network (ieee 802.15.4).
The length of the data-frame is 1000 bits plus 16 bits FCS(Frame Check Sequence), generated by the CRC-CCITT
I know from a research-paper that the CRC-CCITT can detect any 1,2 and 3 bit-errors and any
uneven bit-errors. So only the 4,6,8,.... bit-errors might lead into an undetected error.
To calculate the propability of an undetected error for a data-frame, i would have to
calculate the probability that a 4,6,8,.. bit-error even occurs (given the
bit-error-rate), multiply it by the probability that these specific bit errors actually
lead into an undetected error and sum it all up. for example for 4 bit-errors there exist
1016^4 (simplified) different possible combinations, but only a few of these lead into an
undetected error. (Am I right so far?).
The problem now is, that I don't know how many 4,6,8,.. bit-errors lead into undetected
errors and thus I can't calculate exactly the possibility of an undetected error.
So I made an assumption. In the frame there 2^1000 correct Codewords, that share 2^16
FCS. That means on average 2^1000/2^16 share 1 FCS, but for a specific frame only one is
correct and the others are in incorrect, but are not detectable as such. The total amount
of possible incorrect frames is of cours 2^1016 -1. The average possibility of an
undetected error is the amount of undetectable error devided by the total amount of
errors. (2^984 -1)/(2^1016 -1). Finally I multiplied that by the probability that
error-corruption can even occur as mentioned above and had my results.
I hope I expressed myself coherently. If you have any questions feel free to ask. What I
would like to know is. Does my assumption make sense? And is calculated probality higher
than the actual probability, so that I am still on the safe side.
Do you know where I can get the actual amount of undetectable errors for each bit-error
for my specific data-length CRC-polinomial?
thanks a lot for your time