On the uniqueness of balanced complex orthogonal design

Complex orthogonal designs (CODs) have been used to construct space-time block codes . Its real analog, real orthogonal designs, or equivalently, sum of squares composition formula, have a long history in mathematics. Driven by some practical considerations, Adams et al. (IEEE Trans Info Theory, 57(...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2024-12, Vol.92 (12), p.4169-4187
Main Authors: Gao, Yiwen, Li, Yuan, Kan, Haibin
Format: Article
Language:English
Subjects:
Block codes
Coding and Information Theory
Computer Science
Cryptology
Decoding
Discrete Mathematics in Computer Science
Equivalence
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Summary:Complex orthogonal designs (CODs) have been used to construct space-time block codes . Its real analog, real orthogonal designs, or equivalently, sum of squares composition formula, have a long history in mathematics. Driven by some practical considerations, Adams et al. (IEEE Trans Info Theory, 57(4):2254–2262, 2011) introduced the definition of balanced complex orthogonal designs (BCODs). The code rate of BCODs is 1/2, and their minimum decoding delay is proven to be 2 m , where 2 m is the number of columns. We prove, when the number of columns is fixed, all (indecomposable) balanced complex orthogonal designs (BCODs) have the same parameters [ 2 m , 2 m , 2 m - 1 ] , and moreover, they are all equivalent.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-024-01483-x