Hierarchical Distribution Matching for Probabilistically Shaped Coded Modulation

TL;DR

This paper introduces a hierarchical distribution matching scheme that simplifies implementation and improves efficiency for probabilistic shaping in coded modulation, enabling higher error rates and easier simulation.

Contribution

The paper proposes a fully parallelized, pipelined hierarchical distribution matching scheme that reduces complexity and enhances performance for probabilistic shaping in coded modulation systems.

Findings

HiDM enables efficient DM/invDM with parallel architecture.

It operates at higher post-FEC BER for the same performance.

It slightly increases rate loss and SNR requirements.

Abstract

The implementation difficulties of combining distribution matching (DM) and dematching (invDM) for probabilistic shaping (PS) with soft-decision forward error correction (FEC) coding can be relaxed by reverse concatenation, for which the FEC coding and decoding lies inside the shaping algorithms. PS can seemingly achieve performance close to the Shannon limit, although there are practical implementation challenges that need to be carefully addressed. We propose a hierarchical DM (HiDM) scheme, having fully parallelized input/output interfaces and a pipelined architecture that can efficiently perform the DM/invDM without the complex operations of previously proposed methods such as constant composition DM (CCDM). Furthermore, HiDM can operate at a significantly larger post-FEC bit error rate (BER) for the same post-invDM BER performance, which facilitates simulations. These benefits come at the cost of a slightly larger rate loss and required signal-to-noise ratio at a given post-FEC BER.