Optical Coding Theory with Prime

where the factor 1/2 comes from the assumption of equiprobable data bit-1 and bit-0 transmissions in OOK. In the denominators, p²Φ_{(N, w, 1, 1)OOC} − 1 denotes the number of possible interfering codewords. The first product term accounts for the hit probability of the address codeword (from group i = 0) correlating with an interfering codeword coming from the same (N, w, 1, 1)OOC codeword, without any time shift. The term N represents the number of possible time shifts in a codeword of length N. There are w(p − 1) interfering codewords contributing one-hits. Similarly, the second product term accounts for the case with a time shift, with a probability of w(w − 1)/1N. The factor 1/w represents the probability of getting one-hits from an interfering ...