(Gray) Mappings for Bit-Interleaved Coded Modulation

TLDR

The study examines square QAM mappings for bit‑interleaved coded modulation, building on the 1998 conjecture that Gray labelings maximize achievable capacity. The authors aim to provide construction guidelines that yield capacity‑maximizing Gray mappings. They analyze bit‑level capacities of mappings to identify structural properties and derive the guidelines. They show that Gray mappings are not unique and that the conjecture fails for QAM constellations larger than 16.

Abstract

Mappings for square quadrature amplitude modulation (QAM) are investigated in terms of the achievable capacity in bit-interleaved coded modulation (BICM). In G. Caire et al. (1998) it is conjectured that Gray labelings maximize this capacity. However, Gray mappings are not unique and it can be shown that the conjecture cannot hold in general for QAM constellation sizes larger than 16. Based on the bit level capacities of mappings, structures determining capacity are analyzed. Construction guidelines leading to capacity maximizing Gray mappings are presented.