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This study describes a novel version of digital pulse position modulation (PPM) called offset PPM, which operates at half the line rate of digital PPM and offers an increase in sensitivity. To demonstrate the effectiveness of the technique, theoretical results are presented for an offset PPM system coding 3 bits of pulse code modulation (PCM) data, at a rate of 1 Gbit/s. An optical channel with a Gaussian impulse response, such as that obtained from graded-index plastic optical fibre, was considered. The results are compared to those obtained for digital PPM, using a maximum likelihood sequence detector, and it is shown that offset PPM is more tolerant of pulse dispersion giving a 3.1 dB increase in sensitivity when operating with a channel bandwidth equal to half the PCM bit rate.