Coset Shaping: Constructions and Bounds

TL;DR

The paper introduces coset shaping, a geometric technique for coded QAM and PAM signaling, achieving near-capacity performance with minimal complexity as code length and modulation order increase.

Contribution

It proposes and analyzes coset shaping, a novel geometric shaping method applicable to both information and parity bits without added complexity.

Findings

Gap to capacity can be made arbitrarily small with increasing code length and modulation order.

Provides a Gallager-type bound and numerical performance comparisons.

Effective with both short and mid-length LDPC-coded QAM signaling.

Abstract

A new geometric shaping technique, referred to as coset shaping, is proposed and analyzed for coded QAM and PAM signaling. This method can be applied to both information and parity bits without introducing additional complexity. It is shown that, as the error-correcting code length and the modulation order grow, the gap to capacity of the proposed shaping scheme can be made arbitrarily small. A Gallager-type bound is provided together with numerical results, including performance comparisons for the shaping scheme combined with short and mid-length binary-coded, as well as nonbinary LDPC-coded QAM signaling