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End-to-end Learning of Probabilistic and Geometric Constellation Shaping with Iterative Receivers

Harindu Jayarathne, Dileepa Marasinghe, Nandana Rajatheva, Matti Latva-aho

TL;DR

The paper addresses improving data transmission efficiency by jointly optimizing constellation geometry and symbol probabilities through end-to-end learning with a shaping-encoder assisted transmitter. It introduces two training paradigms, non-IDD and IDD with deep unfolding, to learn constellations and probability distributions that maximize information rate while supporting iterative receivers. Empirical results show learned constellations outperform standard 32-APSK and 32-QAM with BER gains up to 0.3 dB under AWGN and up to 0.1 dB under block fading with perfect CSI, along with notable capacity improvements. These findings demonstrate the viability of end-to-end probabilistic and geometric constellation shaping for practical communication systems employing iterative detection and decoding.

Abstract

An end-to-end learning method for constellation shaping with a shaping-encoder assisted transceiver architecture is presented. The shaping encoder, which produces shaping bits with a higher probability of zeros, is used to produce an efficient symbol probability distribution. Both the probability distribution and the constellation geometry are jointly optimized, using end-to-end learning. Optimized constellations are evaluated using two iterative receiver architectures. Bit error rate (BER) performance gain is quantified against standard amplitude phase-shift keying (APSK) and quadrature amplitude modulation (QAM) constellations. A maximum BER gain of 0.3 dB and 0.15 dB are observed under two receivers for the learned constellations compared to standard APSK or QAM. The basic approach is extended to incorporate the full iterative detection and decoding loop, using the deep unfolding technique. A bit error rate gain of 0.1 dB is observed for the iterative scheme with learned constellations under block fading channel conditions, when compared to standard APSK.

End-to-end Learning of Probabilistic and Geometric Constellation Shaping with Iterative Receivers

TL;DR

The paper addresses improving data transmission efficiency by jointly optimizing constellation geometry and symbol probabilities through end-to-end learning with a shaping-encoder assisted transmitter. It introduces two training paradigms, non-IDD and IDD with deep unfolding, to learn constellations and probability distributions that maximize information rate while supporting iterative receivers. Empirical results show learned constellations outperform standard 32-APSK and 32-QAM with BER gains up to 0.3 dB under AWGN and up to 0.1 dB under block fading with perfect CSI, along with notable capacity improvements. These findings demonstrate the viability of end-to-end probabilistic and geometric constellation shaping for practical communication systems employing iterative detection and decoding.

Abstract

An end-to-end learning method for constellation shaping with a shaping-encoder assisted transceiver architecture is presented. The shaping encoder, which produces shaping bits with a higher probability of zeros, is used to produce an efficient symbol probability distribution. Both the probability distribution and the constellation geometry are jointly optimized, using end-to-end learning. Optimized constellations are evaluated using two iterative receiver architectures. Bit error rate (BER) performance gain is quantified against standard amplitude phase-shift keying (APSK) and quadrature amplitude modulation (QAM) constellations. A maximum BER gain of 0.3 dB and 0.15 dB are observed under two receivers for the learned constellations compared to standard APSK or QAM. The basic approach is extended to incorporate the full iterative detection and decoding loop, using the deep unfolding technique. A bit error rate gain of 0.1 dB is observed for the iterative scheme with learned constellations under block fading channel conditions, when compared to standard APSK.
Paper Structure (11 sections, 8 equations, 7 figures)

This paper contains 11 sections, 8 equations, 7 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Transmitter Design
  4. Receiver Design
  5. End-to-end System Training
  6. Non-IDD Training Architecture
  7. IDD Training Architecture
  8. Results
  9. Non-IDD Training Architecture
  10. IDD Training Architecture
  11. Conclusion

Figures (7)

  • Figure 1: End-to-end architecture of the constellation shaping scheme.
  • Figure 2: The training setup aimed for the simplified receiver. Training is performed between the mapper input and the demapper output.
  • Figure 3: The training setup aimed for the IDD receiver. Training is performed between the mapper input and the demapper output, with both the FEC decoder and the shaping decoder integrated into the model architecture.
  • Figure 4: (a) Learned constellation $T_1$ obtained under the AWGN channel for $S = \{0\}$ system. (b) Learned constellation $T_2$ obtained under AWGN channel for $S = \{0,4\}$ system. The diameter of the symbol points indicates their respective probability of occurrence.
  • Figure 5: Signal-to-noise ratio (SNR) gap to Gaussian channel capacity of BICM capacity for uniform and shaped systems with 32-QAM, 32-APSK and trained constellations.
  • ...and 2 more figures