Effect of binary labeling schemes on PAS with BICM-ID system performance over the AWGN and optical fiber channels

Bit-interleaved coded modulation with iterative decoding (BICM-ID) effectively provides a high spectral efficiency and coding gain for digital coherent systems over additive white Gaussian noise (AWGN) and optical fiber channels. We previously proposed combining probabilistic amplitude shaping (PAS) with BICM-ID to further improve the system performance. However, the BICM-ID performance depends on the binary labeling scheme used for the constellation points. In this study, we evaluated the effect of binary labeling schemes on the performance of the PAS with BICM-ID system. Numerical simulations showed that the PAS with BICM-ID system employing a suitable binary labeling scheme offers a significant coding gain over both the AWGN and optical fiber channels. The system is also robust against performance degradation caused by the optical Kerr effect in the optical fiber channel. We used an extrinsic information transfer (EXIT) chart to analyze the suitability of binary labeling schemes and the effect of bit interleavers. The results showed that a binary labeling scheme is suitable if the slope of the demodulator's EXIT curve is close to the slope of the decoder's EXIT curve. The EXIT chart analysis also showed that inserting bit interleavers mitigates the performance degradation during iterative decoding. In addition, we used bitwise mutual information to evaluate the SNR penalty due to shaping gap and coding gap, and coding gain offered by iterative decoding of BICM-ID.