A family of fast-decodable MIDO codes from crossed-product algebras over &amp;#x211A;

Luzzi, Laura; Oggier, Frédérique

doi:10.1109/isit.2011.6033911

Cited by 15 publications

(17 citation statements)

References 11 publications

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“…In [6], cyclic algebra based codewords are arranged in an Alamouti block code [7] fashion to gain fast decodability for asymmetric space-time codes. Recent fast decodable code constructions include a fully diverse MIDO code conjectured to have the NVD property [8], and MIDO codes with the NVD property based on crossed product algebras [9], [10]. Constructions for arbitrary number of transmit antennas are also available in [11].…”

Section: Introductionmentioning

confidence: 99%

Iterated Space-Time Code Constructions From Cyclic Algebras

Markin

Oggier

2013

IEEE Trans. Inform. Theory

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We propose a full-rate iterated space-time code construction, to design codes of Q-rank 2n from cyclic algebra based codes of Q-rank n. We give a condition for determining whether the resulting codes satisfy the full diversity property, and study their maximum likelihood decoding complexity with respect to sphere decoding. Particular emphasis is given to the asymmetric MIDO (multiple input double output) codes. In the process, we derive an interesting way of obtaining division algebras, and study their center and maximal subfield.

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Section: Introductionmentioning

confidence: 99%

Iterated Space-Time Code Constructions From Cyclic Algebras

Markin

Oggier

2013

IEEE Trans. Inform. Theory

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“…We will assume basic knowledge of central simple algebras (see [15] for instance). Lemmas 7,8,and 9 show us that the existence of (invertible) mutually orthogonal matrices A i , i = 1, . .…”

Section: Azumaya Algebras and Bounds On The Number Of Groupsmentioning

confidence: 99%

“…This then reduces the complexity of decoding from the worst case complexity |S| 2l which arises from a brute-force checking of all 2l-tuples from S, to the order of |S| l ′ for some l ′ < 2l, where l ′ depends on the dimensions of the orthogonal summands. Some examples of recent work on fast decoding include [3], [4], [1], [6], [7], [8], [9], [10], [11]. Many codes have been shown to have reduced decoding complexity; for instance, it is known that the Silver code has a decoding complexity that is no higher than |S| 5 (instead of the possible |S| 8 ) [1, Example 5], considered in Example 2 ahead.…”

Section: Introductionmentioning

confidence: 99%

Bounds on Fast Decodability of Space-Time Block Codes, Skew-Hermitian Matrices, and Azumaya Algebras

Berhuy

Markin

Sethuraman

2015

IEEE Trans. Inform. Theory

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We study fast lattice decodability of space-time block codes for n transmit and receive antennas, written very generally as a linear combination 2l i=1 s i A i , where the s i are real information symbols and the A i are n × n Rlinearly independent complex valued matrices. We show that the mutual orthogonality condition A i A * j + A j A * i = 0 for distinct basis matrices is not only sufficient but also necessary for fast decodability. We build on this to show that for full-rate (l = n 2 ) transmission, the decoding complexity can be no better than |S| n 2 +1 , where |S| is the size of the effective real signal constellation. We also show that for full-rate transmission, g-group decodability, as defined in [1], is impossible for any g ≥ 2. We then use the theory of Azumaya algebras to derive bounds on the maximum number of groups into which the basis matrices can be partitioned so that the matrices in different groups are mutually orthogonal-a key measure of fast decodability. We show that in general, this maximum number is of the order of only the 2-adic value of n. In the case where the matrices A i arise from a division algebra, which is most desirable for diversity, we show that the maximum number of groups is only 4. As a result, the decoding complexity for this case is no better than |S| ⌈l/2⌉ for any rate l.

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“…Fast-decodable codes are treated by Biglieri, Hong and Viterbo [15], Vehkalahti, Hollanti and Oggier [16], [17], Luzzi and Oggier [18], Markin and Oggier [19], and in [13], [14] and [9], to name just a few.…”

Section: Introductionmentioning

confidence: 99%

Fast-decodable MIDO codes from non-associative algebras

Pumplün

Steele

2015

IJICOT

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A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk FAST-DECODABLE MIDO CODES FROM NONASSOCIATIVE ALGEBRAS S. PUMPLÜN AND A. STEELEAbstract. By defining a multiplication on a direct sum of n copies of a given cyclic division algebra, we obtain new unital nonassociative algebras. We employ their left multiplication to construct rate-n and rate-2 fully diverse fast ML-decodable space-time block codes for a multiple input-double output (MIDO) system. We give examples of fully diverse rate-2 4 × 2, 6 × 2, 8 × 2 and 12 × 2 space-time block codes and of a rate-3 6 × 2 code. All are fast ML-decodable. Our approach generalizes the iterated codes in [20].

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A family of fast-decodable MIDO codes from crossed-product algebras over ℚ

Cited by 15 publications

References 11 publications

Iterated Space-Time Code Constructions From Cyclic Algebras

Iterated Space-Time Code Constructions From Cyclic Algebras

Bounds on Fast Decodability of Space-Time Block Codes, Skew-Hermitian Matrices, and Azumaya Algebras

Fast-decodable MIDO codes from non-associative algebras

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