Enhanced LLR for Soft-Decision FEC in Amplified Spatial Division Multiplexing IMDD Systems

We propose an enhanced log-likelihood ratio (E-LLR) technique for soft-decision forward error correction (SD-FEC) in intensity-modulation direct-detection (IMDD) systems with optical amplifiers and demonstrate its effectiveness in 7-core weakly coupled fiber transmission. In amplified IMDD, square-law photodetection and modulator nonlinearities cause amplified spontaneous emission noise to produce non-Gaussian signal statistics, invalidating conventional LLR assumptions and degrading SD-FEC performance. To address this issue, we abandon the classic additive white Gaussian noise (AWGN) model and introduce a channel model based on multi-parameter chi-square distributions that more accurately reflect optical channel noise. Unlike previous Gaussian and chi-square approaches, E-LLR uses a training sequence to estimate the variance and non-centrality parameters for each pulse-amplitude modulation (PAM) level, generating <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> distinct noncentral chi-square distributions for precise LLR computation in FEC decoding. Experimental results show that the proposed approach improves the receiver sensitivity by 1.13dB and reduces the decoding iterations of FEC compared with AWGN-model based schemes. These improvements contribute to reduced system complexity and decoding latency, while still achieving the required bit error rate threshold.