## Description

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].

## Notes

## Parent

## Children

- Frequency-shift keying (FSK) code
- Pulse-position modulation (PPM) code
- Quadrature-amplitude modulation (QAM) code
- Phase-shift keying (PSK) code — PSK is a modulation whose constellation consists of points arranged equidistantly on a circle.

## Cousins

- 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].

## References

- [1]
- J. B. Anderson and A. Svensson, Coded Modulation Systems (Springer US, 2002) DOI
- [2]
- A. Lapidoth, A Foundation in Digital Communication (Cambridge University Press, 2017) DOI
- [3]
- Proakis, John G., and Masoud Salehi. Digital communications. Vol. 4. New York: McGraw-hill, 2001.
- [4]
- 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
- [5]
- 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
- [6]
- 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

- Victor V. Albert (2023-03-05) — most recent

## Cite as:

“Modulation scheme”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/modulation