Divergence-Optimal Fixed-to-Fixed Length Distribution Matching With Shell Mapping

TL;DR

This paper introduces a shell mapping-based fixed-to-fixed length distribution matcher that is optimal for divergence minimization, effectively approximates arbitrary distributions, and enhances performance in low-latency communication scenarios.

Contribution

It presents a divergence-optimal, invertible distribution matching method using shell mapping, applicable to ultra-reliable low-latency communications, outperforming existing methods like CCDM.

Findings

SMDM is optimal for divergence minimization.

SMDM outperforms CCDM by 0.6 dB at 64-QAM.

Effective for short blocklengths in URLLC applications.

Abstract

Distribution matching (DM) transforms independent and Bernoulli(1/2) distributed bits into a sequence of output symbols with a desired distribution. A fixed-to-fixed length, invertible DM architecture based on shell mapping is presented. It is shown that shell mapping for distribution matching (SMDM) is the optimum DM for the informational divergence metric and that finding energy optimal sequences is a special case of divergence minimization. Additionally, it is shown how to find the required shell mapping weight function to approximate arbitrary output distributions. SMDM is combined with probabilistic amplitude shaping (PAS) to operate close to the Shannon limit. SMDM exhibits excellent performance for short blocklengths as required by ultra-reliable low-latency (URLLC) applications. SMDM outperforms constant composition DM (CCDM) by 0.6 dB when used with 64-QAM at a spectral efficiency of 3 bits/channel use and a 5G low-density parity-check code with a short blocklength of 192 bits