Modulation scheme 


A sphere packing mapped into a time-dependent electromagnetic signal [1,2]. There is a close relation between abstract real-space encodings and modulation schemes, and certain simple sphere packings are often synonymous with their corresponding modulation schemes.

Linear modulation schemes encode points into amplitudes of electromagnetic waveforms. Pulse-amplitude modulation (PAM) associates each point with a real-valued amplitude of one quadrature of an electromagnetic waveform [2; Sec. 10.5]. Quadrature amplitude modulation (QAM) associates each pair of points with a complex-valued two-quadrature amplitude of band-limited signal [2; Ch. 16].


See the book [3] for an introduction to modulation schemes.




  • Coherent-state c-q code — Coherent-state c-q codes are modulation schemes to transmission of classical information over quantum analog channels.
  • Coherent-state constellation code — Coherent-state constellation codes are quantum versions of modulation schemes in that their codewords are superpositions of points in a constellation. Additionally, analog codes that achieve AGWN capacity [4] can be used to develop capacity-achieving concatenations of coherent-state constellation codes with quantum polar codes [5,6].


J. B. Anderson and A. Svensson, Coded Modulation Systems (Springer US, 2002) DOI
A. Lapidoth, A Foundation in Digital Communication (Cambridge University Press, 2017) DOI
Proakis, John G., and Masoud Salehi. Digital communications. Vol. 4. New York: McGraw-hill, 2001.
Y. Wu and S. Verdu, “The impact of constellation cardinality on Gaussian channel capacity”, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton) (2010) DOI
F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent-state constellations and polar codes for thermal Gaussian channels”, Physical Review A 95, (2017) arXiv:1603.05970 DOI
F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent state constellations for Bosonic Gaussian channels”, 2016 IEEE International Symposium on Information Theory (ISIT) (2016) DOI
Page edit log

Your contribution is welcome!

on (edit & pull request)— see instructions

edit on this site

Zoo Code ID: modulation

Cite as:
“Modulation scheme”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.
@incollection{eczoo_modulation, title={Modulation scheme}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:

Cite as:

“Modulation scheme”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.