Multilevel (Q-ary, Q > 2) pulse-position modulation (Q-PPM) with direct detection is a very popular transmission method for power-efficient free-space optical communication systems. The combination of Q-PPM with error-control coding is an effective means to further improve power efficiency. In this paper, we study the application of the multilevel coding (MLC) paradigm to Q-PPM transmission. In particular, we devise a powerful coded Q-PPM scheme which is a simplified version of MLC and which we refer to as reduced-level MLC (RL-MLC). We show how to design and optimize RL-MLC for Q-PPM when using constellation-constrained capacity as the pertinent figure of merit. Furthermore, we provide simulative evidence that RL-MLC with off-the-shelf low-density parity-check codes (LDPC) closely approaches its corresponding capacity limit. For 64-PPM, RL-MLC with only two levels achieves practically the same performance as that of bit-interleaved coded modulation with iterative decoding (BICM-ID), which involves a more difficult design procedure.
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