Cyclic Division Algebras: A Tool for Space-Time Coding
نویسندگان
چکیده
منابع مشابه
Cyclic Division Algebras: A Tool for Space-Time Coding
Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requir...
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Coding theory addresses the problem of transmitting information accurately across noisy channels. When a sender transmits a signal s, it will suffer some changes before it reaches the receiver. The receiver then faces the problem of recovering the intended signal, given that he actually received some altered signal r. The challenge of coding theory, then, is to design a system which not only gi...
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Space-time coding is used for reliable high rate transmission over wireless digital channels with multiple antennas at both the transmitter and receiver ends. From a mathematical point of view, a space-time block code (STBC) consists of a family of matrices with complex entries (the codebook) that satisfies a number of properties which determine how well the code performs. The first aim is to f...
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Let F be a number field with ring of integers OF and D a division F -algebra with a maximal cyclic subfield K. We study rings occurring as quotients of a natural OF -order Λ in D by two-sided ideals. We reduce the problem to studying the ideal structure of Λ/qΛ, where q is a prime ideal in OF , s ≥ 1. We study the case where q remains unramified in K, both when s = 1 and s > 1. This work is mot...
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We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D = (K/F, σ, c), employing a K-automorphism τ and an element d ∈ D. These algebras appear in the construction of iterated spacetime block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly lo...
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ژورنال
عنوان ژورنال: Foundations and Trends® in Communications and Information Theory
سال: 2007
ISSN: 1567-2190,1567-2328
DOI: 10.1561/0100000016