Quadratic Forms and Space-Time Block Codes from Generalized Quaternion and Biquaternion Algebras

Abstract

In the context of space-time block codes (STBCs), the theory of generalized quaternion and biquaternion algebras (i.e., tensor products of two quaternion algebras) over arbitrary base fields is presented, as well as quadratic form theoretic criteria to check if such algebras are division algebras. For base fields relevant to STBCs, these criteria are exploited, via Springer's theorem, to construct several explicit infinite families of (bi-)quaternion division algebras. These are used to obtain new $2\x 2$ and $4\x 4$ STBCs.

8 pages, final version

References in corpus (1)

• MMSE Optimal Algebraic Space-Time Codes

Cited by in corpus (6)

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• Iterated Space-Time Code Constructions from Cyclic Algebras
• Revisited Design Criteria For STBCs With Reduced Complexity ML Decoding
• Minimizing the Complexity of Fast Sphere Decoding of STBCs