Probability of error for fault-tolerant byte synchronization detectors

The probability of byte synchronization error (P_SE) for a hard disk drive´s fault-tolerant byte synchronization detector is derived. The P_SE is shown to be a function of the synchronization field length (N), the probability of bit error (p), the threshold of allowable errors (T), the location of the synchronization field within the synchronization detection interval (L) and the minimum Hamming distance (dH_min). The Hamming distance is the number of bits by which a sequence consisting of the synchronization field pattern appended to the preamble of a hard disk drive´s sector header differs from the synchronization field pattern, at each possible relative position. A good value for T is approximately around (dH_m n/-1)/2 bits