Ordered Sequence Detection and Robust Design for Pulse Interval Modulation

This paper proposes an ordered sequence detection (OSD) for digital pulse interval modulation (DPIM) applied in optical wireless communications (OWC). To detect a packet consisting of $L$-chips, the computational complexity of OSD is of the order $\mathcal{O}(L\log_2L)$. Moreover, this paper also proposes a robust pulse interval modulation (RPIM) scheme based on OSD. In RPIM, the last of every $K$ symbols is with more power to transmit information and simultaneously to provide a built-in barrier signal. In this way, error propagation is bounded in a slot of $K$ symbols. Together with interleaver and forward error correction (FEC) codes, the bit error rate (BER) can be greatly reduced. We derive the approximate uncoded BER performance of conventional DPIM with OSD and the newly proposed RPIM with OSD based on order statistic theory. Simulations are conducted to collaborate on theoretical analysis and show that RPIM with OSD considerably outperforms existing DPIM with optimal threshold detection in either uncoded or coded systems over various channels.