Achievable Rates for Probabilistic Shaping

TL;DR

This paper derives achievable rates for layered probabilistic shaping schemes using Gallager's error exponent, discussing various decoding metrics and demonstrating that known rates can be achieved with layered PS, including practical instances like PAS.

Contribution

It introduces a general achievable rate framework for layered probabilistic shaping with various decoding metrics, unifying and extending prior results.

Findings

Achievable rates are derived for layered PS schemes.

Layered PS can achieve previously known rates.

Practical layered PS instances like PAS are discussed.

Abstract

For a layered probabilistic shaping (PS) scheme with a general decoding metric, an achievable rate is derived using Gallager's error exponent approach and the concept of achievable code rates is introduced. Several instances for specific decoding metrics are discussed, including bit-metric decoding, interleaved coded modulation, and hard-decision decoding. It is shown that important previously known achievable rates can also be achieved by layered PS. A practical instance of layered PS is the recently proposed probabilistic amplitude shaping (PAS).