Performance of coded multi-pulse PPM with imperfect slot synchronization in optical direct-detection channel

The performance of coded multi-pulse pulse position modulation (MPPM) consisting of m slots and 2 pulses, denoted as (m, 2) MPPM, with imperfect slot synchronization is analyzed. Convolutional codes and Reed-Solomon (RS) codes are employed for (m, 2) MPPM, and the bit error probability of coded (m, 2) MPPM in the presence of the timing offset is derived. In each coded (m, 2) MPPM, we compare the performance of some different code rate systems. Moreover, we compare the performance of both systems at the same information bit rate. It is shown that in both coded systems, the performance of code rate-1/2 coded MPPM is the best when the timing offset is small. Further, convolutional coded (m, 2) MPPM on the constraint length k⩾7 performs better than Reed-Solomon coded (m, 2) MPPM for the same code rate