Coding for multi-pulse PPM with imperfect slot synchronization in optical direct-detection channels

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 (m, 2) MPPM is the best when the timing offset is small. When the timing offset is somewhat large, however, uncoded (m, 2) MPPM is shown to perform better than coded (m, 2) MPPM. Further, convolutional coded (m, 2) MPPM with the constraint length k≥7 is shown to perform better than RS coded (m, 2) MPPM for the same code rate.