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
- Locally correctable code (LCC)— LCCs can also be defined over the real or complex numbers, and there are no complex 2-query LCCs [1].
- Bosonic code— Bosonic codes are quantum version of analog codes.
Member of code lists
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
Page edit log
- Victor V. Albert (2025-01-02) — most recent
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.