Probabilistically shaped coded modulation for intensity-modulation/direct-detection system

Abstract

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. IM/DD systems have long dominated the short-reach applications due to their simplicity, low-power consumption and cost-effectiveness. In this thesis, I propose and demonstrate an efficient way to apply the PCS technology to IM/DD systems. In the mapping of forward error correction (FEC)-encoded bits onto the pulse amplitude modulation (PAM) symbols, I assign the uniformly distributed parity bits to the least significant bit of binary reflected Gray coding. Then, I 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), I show that the SNR penalty caused by this discrepancy is very small. I evaluate the performance of the proposed scheme for PAM-8 signals using low-density parity-check (LDPC) coding and soft-decision decoding. The achievable information rate, bit-error ratio (BER) after FEC decoding, and frame error ratio after inverse distribution matcher are measured to evaluate the performance of the proposed scheme. The results show that, compared to the uniformly distributed signal, the proposed scheme provides a shaping gain of 1.4 dB. This is also ~1 dB larger than the time-division hybrid modulation. I also carry out the experimental demonstration of the proposed scheme using a 10-Gbaud PAM-8 signal. By using the proposed scheme, I improve the receiver sensitivity by 0.9 dB when compared with the uniformly distributed PAM-8 signal.

Soft-decision decoding might be too power-hungry and expensive to be used for cost-sensitive IM/DD systems. I apply the proposed pairwise distribution and mapping scheme to hard-decision decoding system. For this purpose, I employ the Reed-Solomon (RS) code and PAM-8 modulation. The results obtained from the numerical simulation show that the shaping gains up to 1.0 dB can be obtained when the codeword length of RS code is as long as 4000. I believe that the proposed scheme could be used to improve the data rate or receiver sensitivity of IM/DD systems.