Constant-energy code 

Root code for the Spherical Kingdom


Code whose codewords are points on a real or complex sphere whose radius squared is called the energy. Typically, only angular distances between points are relevant for code performance, so one can normalize codewords of a constant-energy code to obtain up a spherical code, i.e., a constant energy code with energy one.


Constant-energy codes are sphere packings constrained to lie on a sphere, meaning that they can be used to transmit information through the AGWN channel. For a given dimension \(n\), number of codewords \(M\), and average energy \(P\), the constant-energy Gaussian channel coding problem asks to find a set of \(M\) codewords of energy \(nP\) that minimizes the error probability during transmission; see [1; Ch. 3].


See [2; Ch. 7] for more details.


  • Bounded-energy code — Constant-energy codes are bounded-energy codes constrained to lie on a sphere.



  • Quantum spherical code (QSC) — QSCs are quantum analogues of spherical and constant-energy codes because they store information in quantum superpositions of points on a sphere in quantum phase space.


J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI
T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
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Zoo Code ID: points_into_spheres

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“Constant-energy code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
@incollection{eczoo_points_into_spheres, title={Constant-energy code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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Cite as:

“Constant-energy code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.