Here is a list of codes related to modulation schemes.

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Code Description Relation
Binary PSK (BPSK) code Encodes one bit of information into a constellation of antipodal points \(\pm\alpha\) for complex \(\alpha\). These points are typically associated with two phases of an electromagnetic signal.
Coherent-state c-q code Bosonic c-q code whose codewords form a constellation of coherent states. Encodes real numbers into coherent states for transmission over a quantum channel and decoding with a quantum-enhanced receiver. Coherent-state c-q codes are modulation schemes to transmission of classical information over quantum analog channels.
Coherent-state constellation code Qudit-into-oscillator code whose codewords can succinctly be expressed as superpositions of a countable set of coherent states that is called a constellation. Some useful constellations form a group (see gkp, cat or \(2T\)-qutrit codes) while others make up a Gaussian quadrature rule [1,2]. 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 [3] can be used to develop capacity-achieving concatenations of coherent-state constellation codes with quantum polar codes [1,2].
Frequency-shift keying (FSK) code A \(q\)-ary frequency-shift keying (\(q\)-FSK) encodes one \(q\)-ary digit of information into signals with \(q\) different frequencies.
Modulation scheme A sphere packing mapped into a time-dependent electromagnetic signal [4,5]. 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.
Phase-shift keying (PSK) code A \(q\)-ary phase-shift keying (\(q\)-PSK) encodes one \(q\)-ary digit of information into a constellation of \(q\) points distributed equidistantly on a circle in \(\mathbb{C}\) or, equivalently, \(\mathbb{R}^2\). PSK is a modulation whose constellation consists of points arranged equidistantly on a circle.
Pulse-amplitude modulation (PAM) code Encodes a \(q\)-ary digit into a constellation of equally spaced points on the real line. For example, a \(q\)-PAM scheme for \(q=8\) could encode the constellation \(\{ \pm \alpha,\pm 3\alpha,\pm 5\alpha, \pm 7\alpha \}\) with real scaling factor \(\alpha\). The points in the constellation are typically associated with one quadrature of an electromagnetic signal.
Pulse-position modulation (PPM) code An analog code encoding into \(q\) different signals such that each codeword corresponds to a signal.
Quadrature PSK (QPSK) code A quaternary encoding into a constellation of four points distributed equidistantly on a circle. For the case of \(\pi/4\)-QPSK, the constellation is \(\{e^{\pm i\frac{\pi}{4}},e^{\pm i\frac{3\pi}{4}}\}\).
Quadrature-amplitude modulation (QAM) code Encodes into points into a subset of points lying on in \(\mathbb{R}^{2}\), here treated as \(\mathbb{C}\). Each pair of points is associated with a complex amplitude of an electromagnetic signal, and information is encoded into both the norm and phase of that signal [5; Ch. 16].
\(\Lambda_{24}\) Leech lattice Even unimodular lattice in 24 dimensions that exhibits optimal packing. Its automorphism group is the Conway group \(.0\) a.k.a. Co\(_0\). Codewords of the Leech lattice have been proposed to be used for a modulation scheme [6].

References

[1]
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
[2]
F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent state constellations for Bosonic Gaussian channels”, 2016 IEEE International Symposium on Information Theory (ISIT) 2499 (2016) DOI
[3]
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) 620 (2010) DOI
[4]
J. B. Anderson and A. Svensson, Coded Modulation Systems (Springer US, 2002) DOI
[5]
A. Lapidoth, A Foundation in Digital Communication (Cambridge University Press, 2017) DOI
[6]
G. R. Lang and F. M. Longstaff, “A Leech lattice modem”, IEEE Journal on Selected Areas in Communications 7, 968 (1989) DOI