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Information Rates of Approximate Message Passing for Bandlimited Direct-Detection Channels

Daniel Plabst, Mohamed Akrout, Tobias Prinz, Amine Mezghani, Gerhard Kramer

Abstract

The capacity of bandlimited direct-detection channels is challenging to compute or approach due to the receiver non-linearity. A generalized vector approximate message passing (GVAMP) detector is designed to achieve high rates at a reasonable level of complexity. The rates increase by using multi-level coding and successive interference cancellation. The methods are applied to fiber-optic channels with intersymbol interference caused by spectrally efficient pulse shapes, chromatic dispersion, and receiver sampling at twice the baud rate. Bipolar modulation operates within 0.26 bits per channel use (bpcu) of the real-alphabet coherent capacity for optically amplified links, reducing the best-known theoretical gap of 1 bpcu. Remarkably, bipolar modulation achieves 6 dB and 3 dB of power gain over unipolar modulation with and without optical amplification, respectively. Simulations with polar-coded modulation confirm the gains. The GVAMP complexity, measured in multiplications per information bit (mpib), is proportional to the number of iterations and to the logarithm of the block length, and is substantially lower than that of other equalizers. For example, a system with 64-ary bipolar modulation and a root-raised cosine pulse with a 1% roll-off factor was simulated over 4 km of optically amplified standard single-mode fiber in the C-band. The GVAMP receiver requires 93 mpib to achieve 5 bpcu at 300 gigabaud.

Information Rates of Approximate Message Passing for Bandlimited Direct-Detection Channels

Abstract

The capacity of bandlimited direct-detection channels is challenging to compute or approach due to the receiver non-linearity. A generalized vector approximate message passing (GVAMP) detector is designed to achieve high rates at a reasonable level of complexity. The rates increase by using multi-level coding and successive interference cancellation. The methods are applied to fiber-optic channels with intersymbol interference caused by spectrally efficient pulse shapes, chromatic dispersion, and receiver sampling at twice the baud rate. Bipolar modulation operates within 0.26 bits per channel use (bpcu) of the real-alphabet coherent capacity for optically amplified links, reducing the best-known theoretical gap of 1 bpcu. Remarkably, bipolar modulation achieves 6 dB and 3 dB of power gain over unipolar modulation with and without optical amplification, respectively. Simulations with polar-coded modulation confirm the gains. The GVAMP complexity, measured in multiplications per information bit (mpib), is proportional to the number of iterations and to the logarithm of the block length, and is substantially lower than that of other equalizers. For example, a system with 64-ary bipolar modulation and a root-raised cosine pulse with a 1% roll-off factor was simulated over 4 km of optically amplified standard single-mode fiber in the C-band. The GVAMP receiver requires 93 mpib to achieve 5 bpcu at 300 gigabaud.

Paper Structure

This paper contains 66 sections, 145 equations, 23 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Reconstruction Algorithms
  3. Message Passing on Graphs
  4. Expectation Propagation
  5. Approximate Message Passing
  6. Fiber-Optic Communications with DD
  7. Oversampling at the Receiver
  8. Contributions and Organization
  9. Preliminaries
  10. Notation
  11. Gaussian Vectors
  12. Divergence Projections
  13. System Model
  14. Continuous-Time Baseband Model
  15. Discrete-Time Baseband Model
  16. ...and 51 more sections

Figures (23)

  • Figure 1: Model of a short-reach system with DD plabst2022achievable.
  • Figure 2: Spectrum of $|g_\text{tx}\lparen t\rparen|^2$ for a FD-RRC transmit with $\alpha_\text{tx}=1\%$. The dotted lines mark the bandwidth $B_\text{rx} = 2B$ of $g_\text{rx}\lparen t\rparen$.
  • Figure 3: SIC receiver with $S$ stages.
  • Figure 4: Factor graph of GVAMP. Circles and squares represent variable and factor nodes, respectively.
  • Figure 5: GVAMP with an input denoiser (left), LMMSE denoiser (center), and output denoiser (right). The "ext" blocks generate extrinsic messages.
  • ...and 18 more figures