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BICM-compatible Rate Adaptive Geometric Constellation Shaping Using Optimized Many-to-one Labeling

Metodi Plamenov Yankov, Smaranika Swain, Ognjen Jovanovic, Darko Zibar, Francesco Da Ros

Abstract

In this paper, a rate adaptive geometric constellation shaping (GCS) scheme which is fully backward-compatible with existing state of the art bit-interleaved coded modulation (BICM) systems is proposed and experimentally demonstrated. The system relies on optimization of the positions of the quadrature amplitude modulation (QAM) points on the I/Q plane for maximized achievable information rate, while maintaining quantization and fiber nonlinear noise robustness. Furthermore, `dummy' bits are multiplexed with coded bits before mapping to symbols. Rate adaptivity is achieved by tuning the ratio of coded and `dummy' bits, while maintaining a fixed forward error-correction block and a fixed modulation format size. The points' positions and their labeling are optimized using automatic differentiation. The proposed GCS scheme is compared to a time-sharing hybrid (TH) QAM modulation and the now mainstream probabilistic amplitude shaping (PAS) scheme. The TH without shaping is outperformed for all studied data rates in a simulated linear channel by up to 0.7 dB. In a linear channel, PAS is shown to outperform the proposed GCS scheme, while similar performances are reported for PAS and the proposed GCS in a simulated nonlinear fiber channel. The GCS scheme is experimentally demonstrated in a multi-span recirculating loop coherent optical fiber transmission system with a total distance of up to 3000 km. Near-continuous zero-error flexible throughput is reported as a function of the transmission distance. Up to 1-2 spans of increased reach gains are achieved at the same net data rate w.r.t. conventional QAM. At a given distance, up to 0.79 bits/2D symbol of gain w.r.t. conventional QAM is achieved. In the experiment, similar performance to PAS is demonstrated.

BICM-compatible Rate Adaptive Geometric Constellation Shaping Using Optimized Many-to-one Labeling

Abstract

In this paper, a rate adaptive geometric constellation shaping (GCS) scheme which is fully backward-compatible with existing state of the art bit-interleaved coded modulation (BICM) systems is proposed and experimentally demonstrated. The system relies on optimization of the positions of the quadrature amplitude modulation (QAM) points on the I/Q plane for maximized achievable information rate, while maintaining quantization and fiber nonlinear noise robustness. Furthermore, `dummy' bits are multiplexed with coded bits before mapping to symbols. Rate adaptivity is achieved by tuning the ratio of coded and `dummy' bits, while maintaining a fixed forward error-correction block and a fixed modulation format size. The points' positions and their labeling are optimized using automatic differentiation. The proposed GCS scheme is compared to a time-sharing hybrid (TH) QAM modulation and the now mainstream probabilistic amplitude shaping (PAS) scheme. The TH without shaping is outperformed for all studied data rates in a simulated linear channel by up to 0.7 dB. In a linear channel, PAS is shown to outperform the proposed GCS scheme, while similar performances are reported for PAS and the proposed GCS in a simulated nonlinear fiber channel. The GCS scheme is experimentally demonstrated in a multi-span recirculating loop coherent optical fiber transmission system with a total distance of up to 3000 km. Near-continuous zero-error flexible throughput is reported as a function of the transmission distance. Up to 1-2 spans of increased reach gains are achieved at the same net data rate w.r.t. conventional QAM. At a given distance, up to 0.79 bits/2D symbol of gain w.r.t. conventional QAM is achieved. In the experiment, similar performance to PAS is demonstrated.
Paper Structure (19 sections, 7 equations, 15 figures, 2 tables, 1 algorithm)

This paper contains 19 sections, 7 equations, 15 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Rate adaptivity using many to one mapping
  3. Optimization method
  4. Channel model
  5. Achievable information rate
  6. Optimization using automatic differentiation
  7. A comment on the case of non-integer $n_d$
  8. Time-sharing hybrid modulation aspects
  9. A comment on similarities with autoencoders
  10. Results for AWGN channel
  11. Results for the ideal fiber channel model
  12. Experimental setup
  13. Parameter fit of the NLIN model
  14. Channel fit and optimization in practical systems
  15. Zero-codeword argument
  16. ...and 4 more sections

Figures (15)

  • Figure 1: Block diagram of the proposed rate adaptive system.
  • Figure 2: (left axis:) Example target IRs $\eta$ for different choices of the number of dummy bits $N_D$ for $m=8$, $N=64800$ and $K=54000$. (right axis:) minimum change $\eta_{STEP}$ of the target IR.
  • Figure 3: Block diagram of the optimization process. Red, bold arrows indicate the optimization loop.
  • Figure 4: Optimized constellations for MTOM with $n_d=3,2,1,0$ and SNR=13,15,17,19 dB from left to right, respectively.
  • Figure 5: Simulation results for minimum SNR required to achieve the target rate. Top row: assuming ideal FEC based on minimum SNR where AIR $>$ IR; Bottom row: with LDPC FEC, where $BER < 10^{-5}$ at the target IR. Results for 33%, 25% and 20% FEC overhead in the first, second and third column, respectively.
  • ...and 10 more figures