We analyze the error performance of overlapping multipulse pulse position modulation (OMPPM) in optical-direct-detection channel with existing noise. Moreover we analyze the error performance of trellis-coded OMPPM with the small overlap index N=2 in optical direct-detection channel to achieve significant coding gains over uncoded MPPM with the same pulsewidth. First we analyze the block error probability of OMPPM in the background noise case by using the distance defined as the number of nonoverlapping pulsed chips between symbols. Second by using this distance, we partition the OMPPM signals and apply the four-state and the eight-state codes described by Ungerboeck to OMPPM. It is shown that TCM is effective for OMPPM in optical direct-detection channel. The four-state and the eight-state trellis coded OMPPM can achieve gains of 1.56 dB and 3.37 dB over uncoded MPPM at the error probability of 10-6 in background noise case, respectively.