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Improved Lower Bounds on Mutual Information Accounting for Nonlinear Signal-Noise Interaction

Naga V. Irukulapati, Marco Secondini, Erik Agrell, Pontus Johannisson, Henk Wymeersch

TL;DR

The paper addresses the challenge of estimating mutual information in fiber-optic channels by noting that exact channel models are intractable. It introduces a backward-channel AIR framework and uses two variants of stochastic digital backpropagation (SDBP) to construct auxiliary backward channels, comparing them against traditional DBP-based forward-channel bounds. The main contributions are the derivation and estimation of AIRs using backward channels derived from SBS-SDBP and GMP-SDBP, and the demonstration that GMP-SDBP yields up to about 0.7 bit per symbol higher AIR than DBP in nonlinear regimes. These results imply tighter, practically computable lower bounds on the information rate for nonlinear fiber channels, with potential extensions to dual-polarization and more advanced SDBP variants leading to higher achievable rates in real systems.

Abstract

In fiber-optic communications, evaluation of mutual information (MI) is still an open issue due to the unavailability of an exact and mathematically tractable channel model. Traditionally, lower bounds on MI are computed by approximating the (original) channel with an auxiliary forward channel. In this paper, lower bounds are computed using an auxiliary backward channel, which has not been previously considered in the context of fiber-optic communications. Distributions obtained through two variations of the stochastic digital backpropagation (SDBP) algorithm are used as auxiliary backward channels and these bounds are compared with bounds obtained through the conventional digital backpropagation (DBP). Through simulations, higher information rates were achieved with SDBP, {which can be explained by the ability of SDBP to account for nonlinear signal--noise interactions

Improved Lower Bounds on Mutual Information Accounting for Nonlinear Signal-Noise Interaction

TL;DR

The paper addresses the challenge of estimating mutual information in fiber-optic channels by noting that exact channel models are intractable. It introduces a backward-channel AIR framework and uses two variants of stochastic digital backpropagation (SDBP) to construct auxiliary backward channels, comparing them against traditional DBP-based forward-channel bounds. The main contributions are the derivation and estimation of AIRs using backward channels derived from SBS-SDBP and GMP-SDBP, and the demonstration that GMP-SDBP yields up to about 0.7 bit per symbol higher AIR than DBP in nonlinear regimes. These results imply tighter, practically computable lower bounds on the information rate for nonlinear fiber channels, with potential extensions to dual-polarization and more advanced SDBP variants leading to higher achievable rates in real systems.

Abstract

In fiber-optic communications, evaluation of mutual information (MI) is still an open issue due to the unavailability of an exact and mathematically tractable channel model. Traditionally, lower bounds on MI are computed by approximating the (original) channel with an auxiliary forward channel. In this paper, lower bounds are computed using an auxiliary backward channel, which has not been previously considered in the context of fiber-optic communications. Distributions obtained through two variations of the stochastic digital backpropagation (SDBP) algorithm are used as auxiliary backward channels and these bounds are compared with bounds obtained through the conventional digital backpropagation (DBP). Through simulations, higher information rates were achieved with SDBP, {which can be explained by the ability of SDBP to account for nonlinear signal--noise interactions

Paper Structure

This paper contains 14 sections, 17 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Lower bounds on mutual information
  3. Lower Bounds using Auxiliary Forward Channel $q(\mathbf{y}|\mathbf{x})$
  4. Lower Bounds using Auxiliary Backward Channel $r(\mathbf{x}|\mathbf{y})$
  5. Monte Carlo Estimation of AIR
  6. Computation of AIR for the fiber-optic channel
  7. Computation of AIR using DBP
  8. Computation of AIR using SDBP
  9. Numerical Results and Discussion
  10. System Parameters
  11. Results
  12. Discussion
  13. Conclusion
  14. Acknowledgments

Figures (5)

  • Figure 1: Auxiliary channels obtained for the fiber-optic channel using two variations of SDBP, and DBP, where $x_k \in \Omega$. The distribution $\tilde{r}_k(\cdot|\mathbf{y})$ is evaluated at $x_k \in \Omega$, multiplied with the prior, and normalized to get an auxiliary backward channel, ${r}_k(\cdot|\mathbf{y})$. MF refers to the matched filter.
  • Figure 2: A fiber link with $N$ spans where each span consists of an single mode fiber, fiber Bragg grating, and erbium-doped fiber amplifers (EDFA).
  • Figure 3: AIR using DBP-iidG Secondini2013Fehenberger2015a, DBP-CG Eriksson2016, SBS-SDBP Irukulapati2014TCOM, and GMP-SDBP Wymeersch2015SPAWC for 14 GBd, 64-QAM, fiber Bragg grating link, $N=30$, $L=120$ km. FOC refers to fiber-optic channel.
  • Figure 4: Maximum AIR (obtained at optimum power) for diferent number of spans for 14 GBd, 64-QAM, and $L=100$ km.
  • Figure 5: The gains in AIR of GMP-SDBP (resp. SBS-SDBP) over DBP-CG are shown using solid (resp. dashed) lines for 64-QAM, $L=100$ km for 28 GBd (diamonds) and 56 GBd (circles).