Replacing the Soft FEC Limit Paradigm in the Design of Optical Communication Systems

TL;DR

The paper tackles the widespread SD-FEC limit design paradigm in optical communications and demonstrates that channel-independent FEC limits fail for soft-decision bit-wise decoding, especially at low code rates and with high-order modulations. It advocates the generalized mutual information (GMI) as a universal predictor of post-FEC BER, deriving achievable-rate bounds for memoryful and memoryless channels and showing that GMI, computed from bit-wise L-values, aligns with actual decoder performance across AWGN and nonlinear optical channels. Through extensive simulations (AWGN and NLSE) and experiments (64QAM WDM), the authors show that GMI consistently predicts post-FEC BER for both LDPC and turbo codes, while pre-FEC BER and ordinary MI can mislead across varying modulations and code rates. They propose replacing the traditional SD-FEC limit with a GMI-based limit, highlighting practical implications for spectral-efficiency estimates and system design in coherent optical networks, with caveats for iterative or nonbinary decoding scenarios.

Abstract

The FEC limit paradigm is the prevalent practice for designing optical communication systems to attain a certain bit-error rate (BER) without forward error correction (FEC). This practice assumes that there is an FEC code that will reduce the BER after decoding to the desired level. In this paper, we challenge this practice and show that the concept of a channel-independent FEC limit is invalid for soft-decision bit-wise decoding. It is shown that for low code rates and high order modulation formats, the use of the soft FEC limit paradigm can underestimate the spectral efficiencies by up to 20%. A better predictor for the BER after decoding is the generalized mutual information, which is shown to give consistent post-FEC BER predictions across different channel conditions and modulation formats. Extensive optical full-field simulations and experiments are carried out in both the linear and nonlinear transmission regimes to confirm the theoretical analysis.

Figures (10)

• Figure 1: Dual-polarization CM transceiver with SD-FEC under consideration. The transmitter for each polarization consists of two cascaded binary FEC encoders followed by an $M$QAM mapper. The receiver is a BW receiver: L-values are calculated by the demapper (ignoring the intersymbol and interpolarization interference), which is followed by an SD-FEC decoder and an HD-FEC decoder.
• Figure 2: Interface for (a) the inner SD-FEC and (b) the outer HD-FEC in Fig. \ref{['model_general_2pol']} (for one polarization). The BISO channel characterized by the GMI and the BSC by its crossover probability given by the BER after SD-FEC decoding ${\textnormal{BER}}_{{\textnormal{post}}}$.
• Figure 3: Post-FEC BER for TCs with $R_\mathrm{c}\in\{2/5,1/2,3/5,2/3,3/4,5/6\}$ (colors) and different modulation formats (markers): $4$QAM, $8$QAM, $64$QAM, and $256$QAM. The post-FEC BER is shown versus (a) pre-FEC BER, (b) normalized MI, and (c) normalized GMI. The L-values for $8$QAM and for $256$QAM are calculated using the max-log approximation.
• Figure 4: Conditional PDF of the L-values $f_{L|B}(l|1)$ in \ref{['GMI.LLRs.Symm.Mix.PDF']} for $8$QAM and $64$QAM. In both cases the L-values are calculated using \ref{['LLR.sum-exp.AWGN']}.
• Figure 5: Required values for the different metrics to give ${\textnormal{BER}}_{{\textnormal{post}}}=4.7\cdot 10^{-3}$ as a function of the code rate for the same cases as in Fig. \ref{['BERout_TC']}: (a) normalized MI and (b) normalized GMI. The curves $I(X;Y)=mR_\mathrm{c}$ and ${\textnormal{GMI}}=mR_\mathrm{c}$ are shown in (a) and (b), resp.