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Stochastic Digital Backpropagation with Residual Memory Compensation

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

TL;DR

This work extends stochastic digital backpropagation (SDBP) by explicitly modeling residual memory in fiber-optic receivers using two approaches: a memory-aware Viterbi-based detector (VA-SDBP) and a decision-directed detector (DD-SDBP). By representing intermediate uncertainties with particle distributions and employing Gaussian approximations for marginal messages, the methods compute a MAP-like decision on sequences, significantly reducing symbol error rate (SER) versus traditional DBP and SBS-SDBP, especially in dispersion-managed links. VA-SDBP achieves the best performance, but its complexity grows exponentially with memory length $L$, while DD-SDBP offers a practical trade-off with causal memory. The results indicate NSNI and memory effects are crucial in inline DM systems, with gains up to 10× for QPSK and 14× for 16-QAM, suggesting memory-aware FG-based detectors as a promising direction for high-spectral-efficiency fiber communications.

Abstract

Stochastic digital backpropagation (SDBP) is an extension of digital backpropagation (DBP) and is based on the maximum a posteriori principle. SDBP takes into account noise from the optical amplifiers in addition to handling deterministic linear and nonlinear impairments. The decisions in SDBP are taken on a symbol-by-symbol (SBS) basis, ignoring any residual memory, which may be present due to non-optimal processing in SDBP. In this paper, we extend SDBP to account for memory between symbols. In particular, two different methods are proposed: a Viterbi algorithm (VA) and a decision directed approach. Symbol error rate (SER) for memory-based SDBP is significantly lower than the previously proposed SBS-SDBP. For inline dispersion-managed links, the VA-SDBP has up to 10 and 14 times lower SER than DBP for QPSK and 16-QAM, respectively.

Stochastic Digital Backpropagation with Residual Memory Compensation

TL;DR

This work extends stochastic digital backpropagation (SDBP) by explicitly modeling residual memory in fiber-optic receivers using two approaches: a memory-aware Viterbi-based detector (VA-SDBP) and a decision-directed detector (DD-SDBP). By representing intermediate uncertainties with particle distributions and employing Gaussian approximations for marginal messages, the methods compute a MAP-like decision on sequences, significantly reducing symbol error rate (SER) versus traditional DBP and SBS-SDBP, especially in dispersion-managed links. VA-SDBP achieves the best performance, but its complexity grows exponentially with memory length , while DD-SDBP offers a practical trade-off with causal memory. The results indicate NSNI and memory effects are crucial in inline DM systems, with gains up to 10× for QPSK and 14× for 16-QAM, suggesting memory-aware FG-based detectors as a promising direction for high-spectral-efficiency fiber communications.

Abstract

Stochastic digital backpropagation (SDBP) is an extension of digital backpropagation (DBP) and is based on the maximum a posteriori principle. SDBP takes into account noise from the optical amplifiers in addition to handling deterministic linear and nonlinear impairments. The decisions in SDBP are taken on a symbol-by-symbol (SBS) basis, ignoring any residual memory, which may be present due to non-optimal processing in SDBP. In this paper, we extend SDBP to account for memory between symbols. In particular, two different methods are proposed: a Viterbi algorithm (VA) and a decision directed approach. Symbol error rate (SER) for memory-based SDBP is significantly lower than the previously proposed SBS-SDBP. For inline dispersion-managed links, the VA-SDBP has up to 10 and 14 times lower SER than DBP for QPSK and 16-QAM, respectively.

Paper Structure

This paper contains 11 sections, 9 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Factor Graphs for Receiver Design
  3. System Model
  4. SDBP and Proposed Approaches
  5. SDBP
  6. VA-SDBP
  7. DD-SDBP
  8. Numerical Simulations and Discussion
  9. Simulation Setup and Performance Metrics
  10. Results and Discussion
  11. Conclusions

Figures (3)

  • Figure 1: A fiber link with $N$ spans where each span consists of an SMF, a DCM module (for DM links), and EDFAs.
  • Figure 2: SER as a function of input power for 56 Gbaud, FBG as DCM, for (a) QPSK and (b) 16-QAM. Solid (resp. dashed) lines in VA-SDBP and DD-SDBP represent cases when $L=1$ (resp. $L=2$).
  • Figure 3: Gains in SER for the proposed algorithms compared to DBP.

Theorems & Definitions (2)

  • Definition 1: Particle representation of a distribution
  • Definition 2: Distributions associated with particles