Let's say I have a data stream of bits in which I'm attempting to detect a sixteen bit sync pattern (The pattern is FB28 or 1111 1011 0010 1000 in binary, if that matters)
If I allow a one bit error in the pattern to still be considered a match (e.g. EB28), what are the odds of a false positive?
I know that, if I confine the error to a single bit (say the high bit), the odds are 1 in 2^15 (or one in 32768), but if any bit can be in error, is it simply 32768 / 16? Or is it a combination/permutation problem?