Alternative Names: Quadrature-amplitude modulation (QAM) code, Quadrature-amplitude modulation (QAM) scheme, Quadrature-amplitude modulation (QAM) signaling format.
Description
Encodes into a finite set of points in \(\mathbb{R}^{2}\), often treated as \(\mathbb{C}\). Each point is associated with a complex amplitude of an electromagnetic signal, so information is encoded jointly in the in-phase and quadrature components [1; Ch. 16].
QAM schemes with \(q\) constellation points are often called \(q\)-QAM, and \(q\) is often chosen as a power of two to facilitate concatenation with a binary code.
Rate
High-order QAM, especially with appropriate shaping and coding, can operate close to Shannon AWGN capacity at high signal-to-noise ratio [2; Fig. 11.8].Realizations
Optical communication (e.g., Ref. [3]).Telephone-line modems: 1971 Codex 9600C and international standard V.29 used 16-QAM [4].Cousins
- Lattice— QAM encodings often consist of lattice constellations, i.e., finite sets of points scooped out of an infinite 2D lattice.
- Gottesman-Kitaev-Preskill (GKP) code— Finite-energy GKP codes are quantum counterparts of lattice-based QAM codes in that both use a subset of points on a lattice.
- Gray code— 2D Gray codes are often concatenated with \(n=1\) lattice-based QAM codes so that the Hamming distance between the bitstrings encoded into the points is a discretized version of the Euclidean distance between the points.
- Hyperbolic sphere packing— Hyperbolic QAM constellations may yield improved performance over Euclidean ones [5].
- Turbo code— Turbo codes concatenated with QAM codes offer a substantial coding gain [6].
Primary Hierarchy
Parents
Quadrature-amplitude modulation (QAM) format
Children
PAM codes can be thought of as QAM codes restricted to the real line. A \(q\times q\)-QAM code is informationally equivalent to two \(q\)-PAM codes.
References
- [1]
- A. Lapidoth, A Foundation in Digital Communication (Cambridge University Press, 2017) DOI
- [2]
- R. E. Blahut, Modem Theory (Cambridge University Press, 2009) DOI
- [3]
- F. Buchali, F. Steiner, G. Bocherer, L. Schmalen, P. Schulte, and W. Idler, “Rate Adaptation and Reach Increase by Probabilistically Shaped 64-QAM: An Experimental Demonstration”, Journal of Lightwave Technology 34, 1599 (2016) DOI
- [4]
- International Telecommunication Union-T, Recommendation V.29: 9600 Bits Per Second Modem Standardized For Use on Point-to-Point 4-Wire Leased Telephone-Tpe Circuits, 1993
- [5]
- E. B. Silva, R. Palazzo Jr., and M. Firer, “Performance analysis of QAM-like constellations in hyperbolic space”, 2000 International Symposium on Information Theory and its Applications, Honolulu, USA. 2000
- [6]
- S. Le Goff, A. Glavieux, and C. Berrou, “Turbo-codes and high spectral efficiency modulation”, Proceedings of ICC/SUPERCOMM’94 - 1994 International Conference on Communications 645 DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2022-11-07)
Cite as:
“Quadrature-amplitude modulation (QAM) format”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/qam, arXiv:2606.11484
Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/analog/modulation/qam.yml.