If we have a large file, I want to know how this will affect the probability of undetected errors, especially in CRCs. I know that undetected error rate (packet or chunk) is= BitR* BER * 0.5^k which K is the FSC of the CRC. in CRC 32 k is 31,
from this equation and picture below, the packet size is not effecting the probability of undetected error for different packet sizes. Suppose we have 1,000,000 packets each with 2^(-32) probability of undetected error, how can I calculate the probability of undetected error for the entire 1Petabyte file?
The formula for mis-detection rate for multiple packets generally involves calculating the probability of 1 minus probability of zero mis-dectections. Assuming that the packet mis-detected rate is (1/(2^32)), then the mis-detected rate for 1000000 packets is 1-((1-(1/(2^32)))^1000000) ~= 1 - (0.999999999767169356346^1000000) ~= 0.0002328.