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Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping.

Yunus Can Gültekin1, Tobias Fehenberger2, Alex Alvarado1

  • 1Signal Processing Systems Group, Information and Communication Theory Lab, Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.

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Summary
This summary is machine-generated.

For short blocklengths, sphere shaping (SpSh) offers superior energy efficiency over distribution matching (DM) techniques like constant composition distribution matching (CCDM). SpSh minimizes rate loss, improving power efficiency by up to 1 dB for additive white Gaussian noise channels.

Keywords:
constellation shapingdistribution matchingprobabilistic amplitude shapingshaping gapsphere shaping

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Area of Science:

  • Digital Communications
  • Information Theory
  • Signal Processing

Background:

  • Probabilistic amplitude shaping (PAS) is crucial for optimizing communication systems.
  • Traditional distribution matching (DM) algorithms, like constant composition distribution matching (CCDM), face efficiency limitations at short blocklengths due to rate loss.
  • The objective for short blocklengths shifts from strict distribution matching to maximizing energy efficiency within the signal space.

Purpose of the Study:

  • To systematically compare distribution matching (DM) and sphere shaping (SpSh) for short blocklength PAS.
  • To evaluate energy efficiency and rate loss of different shaping algorithms over additive white Gaussian noise (AWGN) channels.
  • To analyze the end-to-end decoding performance and computational complexity of these techniques.

Main Methods:

  • Comparative analysis of CCDM, multiset-partition DM (MPDM), and SpSh algorithms.
  • Numerical simulations to assess rate loss and power efficiency.
  • End-to-end decoding performance simulations for blocklengths around 200.
  • Discussion on algorithmic complexity (latency, storage, computations).

Main Results:

  • MPDM and SpSh demonstrate reduced rate loss compared to CCDM for short blocklengths.
  • SpSh achieves the minimum rate loss, particularly for ultra-short blocklengths, by prioritizing energy efficiency.
  • Up to 1 dB power efficiency improvement over uniform signaling is observed with MPDM and SpSh at blocklengths around 200.

Conclusions:

  • For short blocklength PAS over AWGN channels, energy-efficient signal space design (SpSh, MPDM) is more effective than traditional distribution matching (CCDM).
  • Sphere shaping (SpSh) offers the best performance in terms of minimizing rate loss and maximizing power efficiency.
  • The choice of algorithm impacts latency, storage, and computational complexity, requiring consideration for practical implementation.