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. Wheji 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 k7 is shown to perform better than RS coded (m, 2) MPPM for the same code rate.

The performance of multi-pulse pulse position modulation (MPPM) consisting of m slots and 2 pulses, denoted as (m, 2) MPPM, with imperfect slot synchronization is analyzed. The word error probability of (m, 2) MPPM in the presence of timing offset is analyzed, and the optimum symbol sets of (m, 2) MPPM minimizing the symbol error probability are assigned. When an unassigned symbol is detected, the receiver decodes the unassigned symbol as one of the assigned symbols having the highest probability of transition from the assigned symbol to the unassigned symbol. The bit error probability of (m, 2) MPPM in the presence of the timing offset is analyzed, and the bit error probability of (m, 2) MPPM is compared with that of PPM for the same transmission bandwidth and the same transmission rate. Moreover, the bit error probability of (m, 2) MPPM synchronized by a phase-locked loop (PLL) is also analyzed. It is shown that a word with two continuous pulses has better performance than a word with two separate pulses. It is also shown that when the timing offset occurs, and when the slot clock is synchronized by a PLL, (m, 2) MPPM performs better than PPM because (m, 2) MPPM has the optimum assigned symbols, and can decode detected words more correctly than PPM.