Modulation scheme 

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

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

Parent

Children

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. K. Wolf et al., editors , Coded Modulation Systems (Kluwer Academic Publishers, 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
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Zoo Code ID: modulation

Cite as:
“Modulation scheme”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/modulation
BibTeX:
@incollection{eczoo_modulation,
  title={Modulation scheme},
  booktitle={The Error Correction Zoo},
  year={2023},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/modulation}
}
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Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/analog/modulation/modulation.yml.