Probabilistically shaped coded modulation for IM/DD system

The probabilistic constellation shaping (PCS) technology has recently gained a great deal of attention for coherent optical communication systems since it allows us to approach the Shannon capacity limit by varying the symbol distribution adaptively to the signal-to-noise ratio (SNR). However, there is a lack of literature on how to apply this technology to intensity modulation (IM)/direct detection (DD) systems. In this paper, we propose and demonstrate an efficient way to apply the PCS technology for IM/DD systems. In the mapping of forward error correction-encoded bits onto the pulse amplitude modulation (PAM) symbols, we assign the uniformly distributed bits to the least significant bit of binary reflected Gray coding. Then, we have a pairwise distribution of symbol amplitude, where two adjacent symbols have the same probability. Although this distribution deviates from the optimum distribution (such as Maxwell-Boltzmann distribution), we show that the SNR penalty caused by this discrepancy is negligible. We evaluate the performance of the proposed scheme through simulation by measuring the achievable rate and frame error ratios after inverse distribution matcher. The results show that the proposed scheme provides a shaping gain larger than the time-division hybrid modulation. We also carry out the experimental demonstration of the proposed scheme using a 10-Gbaud PAM-8 signal. By using the proposed scheme, we improve the receiver sensitivity by 0.9 dB when compared with the uniformly distributed PAM-8 signal.