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Analog code

Alternative names: Code over \(\mathbb{R}\).
Root code for the Analog Kingdom

Description

Encodes states (codewords) into coordinates in the \(n\)-dimensional (real or complex) coordinate space (\(\mathbb{R}^n\) or \(\mathbb{C}^n\)). Codes for storing discrete sets of symbols include sphere packings, tilings, and any other codes that use real or complex numbers for encoding. The number of codewords may be infinite because the coordinate space is infinite, so various restricted versions have to be constructed in practice.

Cousins

Primary Hierarchy

Parents
Analog code alphabets, \(\mathbb{R}^n\) or \(\mathbb{C}^n\), are infinite fields, which are groups under addition.
Analog code
Children
Bounded-energy codes are analog codes constrained to lie on or inside a sphere.
Real-number block codes encode continuous sets of real or complex numbers into a real or complex vector space.

References

[1]
B. Barak, Z. Dvir, A. Wigderson, and A. Yehudayoff, “Rank Bounds for Design Matrices with Applications to Combinatorial Geometry and Locally Correctable Codes”, (2011) arXiv:1009.4375
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Zoo Code ID: analog

Cite as:
“Analog code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/analog
BibTeX:
@incollection{eczoo_analog, title={Analog code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/analog} }
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Permanent link:
https://errorcorrectionzoo.org/c/analog

Cite as:

“Analog code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/analog

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