arXiv:2608.20102v3 Announce Type: replace Abstract: The demand for higher speeds in intra-data center interconnects will eventually require high-order pulse amplitude modulation (PAM) combined with soft-decision (SD) forward error correction (FEC). The laser relative intensity noise (RIN) is an important noise impairment that limits the performance of high-speed intensity-modulation (IM) and direct-detection (DD) systems, as it induces a channel with signal-dependent noise. In this paper, we show that an accurate calculation of the log-likelihood ratios (LLRs) is critical for the performance of the SD-FEC decoder in RIN-dominated IM-DD systems. First, we show that assuming signal-independent additive white Gaussian noise (AWGN) statistics to compute LLRs results in a significant penalty in performance. As an alternative, we propose a low-complexity piecewise linear approximation of the exact LLRs of Gray-coded PAM-4 and PAM-8 for the RIN-dominated IM-DD channel. We show using the generalized mutual information that our approximation results in no performance loss versus using exact LLRs, unlike the AWGN-like assumption. Furthermore, we validate the analysis with bit error rate (BER) performance of SD decoding. We show that our approximation matches the BERs achieved using exact LLRs. Therefore, our approximation avoids a BER error floor penalty of up to 7.2 times using an extended Hamming code with PAM-4, and up to 2.41 dB of optical modulation amplitude penalty using high-code-rate low-density parity-check codes with PAM-8 for the same target BER.