Post-FEC BER Benchmarking for Bit-Interleaved Coded Modulation with Probabilistic Shaping

TL;DR

This work addresses post-FEC BER benchmarking for bit-interleaved coded modulation with probabilistic shaping by introducing generalized L-values under mismatched decoding and linking NGMI, ASI, and achievable FEC rate. It shows these metrics are equivalent under matched decoding and then assesses approximate equivalence in practical PAS scenarios, including nonlinear fiber channels. The results demonstrate that ASI provides a robust correlation with post-FEC BER, outperforming pre-FEC BER, while highlighting bit-mapping sensitivity and the stabilizing effect of random or unstructured mappings. The findings offer practical guidance for benchmarking PAS-based systems in both Gaussian and nonlinear fiber contexts, and quantify the trade-offs introduced by shaping, decoding, and channel nonidealities.

Abstract

Accurate performance benchmarking after forward error correction (FEC) decoding is essential for system design in optical fiber communications. Generalized mutual information (GMI) has been shown to be successful at benchmarking the bit-error rate (BER) after FEC decoding (post-FEC BER) for systems with soft-decision (SD) FEC without probabilistic shaping (PS). However, GMI is not relevant to benchmark post-FEC BER for systems with SD-FEC and PS. For such systems, normalized GMI (NGMI), asymmetric information (ASI), and achievable FEC rate have been proposed instead. They are good at benchmarking post-FEC BER or to give an FEC limit in bit-interleaved coded modulation (BICM) with PS, but their relation has not been clearly explained so far. In this paper, we define generalized L-values under mismatched decoding, which are connected to the GMI and ASI. We then show that NGMI, ASI, and achievable FEC rate are theoretically equal under matched decoding but not under mismatched decoding. We also examine BER before FEC decoding (pre-FEC BER) and ASI over Gaussian and nonlinear fiber-optic channels with approximately matched decoding. ASI always shows better correlation with post-FEC BER than pre-FEC BER for BICM with PS. On the other hand, post-FEC BER can differ at a given ASI when we change the bit mapping, which describes how each bit in a codeword is assigned to a bit tributary.

Figures (8)

• Figure 1: System model of BICM with PS. Here we show the notations of the signals with the number of the dimensions and key performance metrics that will be discussed in this paper.
• Figure 2: An example of pdfs in the case of PAS-64-QAM (system (i) in Tab. \ref{['tab:sim_8PAM']}) at a SNR of 9 dB: (a) $p_{B,L}(b,l)$, (b) $p_{L_{\text{a}}}(l)$, and (c) $p_{|L_{\text{a}}|}(l)$. The high peaks are due to clipping the pdf by a finite range histogram. The effect of the clipping at large $L_{\text{a}}$ in (b) is negligible for calculating the ASI under a reasonable scaling of the L-values.
• Figure 3: ASI as a function of SNR. The vertical axis is scaled according to $\log_{10} ( -\log_{10} (1-\text{ASI}))$ to make the QPSK-curve nearly linear. An alternative way to realize this linearization would be to plot $J^{-1}(\text{ASI})$, where $J(\cdot)$ denotes the J-function, used in tenbrink_2004.
• Figure 4: Post-SD-FEC BER with fixed structured bit mappings. (a) and (b) are with $\mathbb{M}_{\text{FS1}}$, (c) and (d) are with $\mathbb{M}_{\text{FS2}}$. The dependence on pre-FEC BER is shown in (a) and (c), and on ASI in (b) and (d).
• Figure 5: Post-SD-FEC BER with random ($\mathbb{M}_{\text{R}}$) or fixed unstructured ($\mathbb{M}_{\text{FU}}$) bit mappings. (a) and (b) are with $\mathbb{M}_{\text{R}}$, (c) and (d) are with $\mathbb{M}_{\text{FU}}$. The dependence on pre-FEC BER is shown in (a) and (c), and on ASI in (b) and (d).

Theorems & Definitions (3)

• Theorem 1
• Theorem 2
• Theorem 3