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Hierarchical Distribution Matching for Probabilistic Amplitude Shaping.

Stella Civelli^1,2, Marco Secondini^1,2

¹Tecip Institute, Scuola Superiore Sant'Anna, 56124 Pisa, Italy.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

A new hierarchical distribution matcher (Hi-DM) approach combines multiple DMs for enhanced performance and flexibility in coded modulations. This method achieves the benefits of long DMs with the efficiency of shorter ones.

Keywords:

coded modulation constant composition constellation shaping distribution matcher probabilistic shaping pulse position modulation shaping gain sphere shaping

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Area of Science:

Optical communication systems
Information theory

Background:

Probabilistic amplitude shaping (PAS) via distribution matchers (DMs) improves coded modulation performance and flexibility.
Existing DM structures face a trade-off between performance and complexity, often increasing with block length.

Purpose of the Study:

Introduce a hierarchical distribution matcher (Hi-DM) to achieve high performance with low complexity.
Explore the structure, properties, and encoding/decoding procedures of Hi-DM.
Evaluate the performance of specific Hi-DM configurations.

Main Methods:

Developed a layered Hi-DM architecture where upper layers process sequences of lower-layer DMs as virtual symbols.
Designed and analyzed three specific Hi-DM configurations.
Compared Hi-DM performance against single-layer DMs in terms of rate loss and energy loss.

Main Results:

A two-layer Hi-DM using constant composition DMs (CCDM) achieved a 0.19dB SNR gain over a single-layer CCDM with similar complexity.
A Hi-DM using minimum-energy lookup tables offered a 0.12dB gain and reduced complexity compared to a single-layer enumerative sphere shaping DM with equivalent memory.

Conclusions:

The proposed Hi-DM approach effectively balances performance and complexity in bandwidth-efficient coded modulations.
Hi-DM offers a practical solution for enhancing optical communication systems by leveraging layered DM structures.