Space-Time Codes from Crossed Product Algebras of Degree 4

Berhuy, Grégory; Oggier, Frédérique

doi:10.1007/978-3-540-77224-8_13

Cited by 10 publications

(15 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 5: Note that the case when τ = σ and both are Galois automorphisms of K of order 2, the iterated construction coming from α θ (D, D) is in fact the same as the matrix representation of the crossed product (K/F, γ, θ, 1) [18] induced by left multiplication, where the automorphisms σ, τ generate the biquadratic extension K/F and D = (K/K σ , σ, γ).…”

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

Iterated Space-Time Code Constructions From Cyclic Algebras

Markin

Oggier

2013

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

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.

show abstract

Section: Remarkmentioning

confidence: 99%

“…from which it is clear that the orthogonal relations among D j determine those among B j . The other equality is handled similarly, using (18).…”

Section: Remarkmentioning

confidence: 99%

Iterated Space-Time Code Constructions From Cyclic Algebras

Markin

Oggier

2013

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…As shown in [1], u is such that N L/K (u) = 1, and suitable a and b are determined by the choice of u in the following way:…”

Section: Such An Algebra Is Of the Formmentioning

confidence: 99%

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

Luzzi

Oggier

2011

2011 IEEE International Symposium on Information Theory Proceedings

View full text Add to dashboard Cite

Multiple Input Double Output (MIDO) asymmetric space-time codes for 4 transmit antennas and 2 receive antennas can be employed in the downlink from base stations to portable devices. Previous MIDO code constructions with low Maximum Likelihood (ML) decoding complexity, full diversity and the nonvanishing determinant (NVD) property are mostly based on cyclic division algebras. In this paper, a new family of MIDO codes with the NVD property based on crossed-product algebras over Q is introduced. Fast decodability follows naturally from the structure of the codewords which consist of four generalized Alamouti blocks. The associated ML complexity order is the lowest known for full-rate MIDO codes (O(M 10 ) instead of O(M 16 ) with respect to the real constellation size M ). Numerical simulations show that these codes have a performance from comparable up to 1dB gain compared to the best known MIDO code with the same complexity.

show abstract

“…for instance [1], [2], [3], [4], [5], [6], [7]). Similarly built nonassociative division algebras can also be used in code design, see for instance [8], [9], [10] or [11].…”

Section: Introductionmentioning

confidence: 99%

Fast-decodable MIDO codes from non-associative algebras

Pumplün

Steele

2015

IJICOT

View full text Add to dashboard Cite

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].

show abstract

Space-Time Codes from Crossed Product Algebras of Degree 4

Cited by 10 publications

References 8 publications

Iterated Space-Time Code Constructions From Cyclic Algebras

Iterated Space-Time Code Constructions From Cyclic Algebras

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

Fast-decodable MIDO codes from non-associative algebras

Contact Info

Product

Resources

About

Space-Time Codes from Crossed Product Algebras of Degree 4

Cited by 10 publications

References 8 publications

Iterated Space-Time Code Constructions From Cyclic Algebras

Iterated Space-Time Code Constructions From Cyclic Algebras

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

Fast-decodable MIDO codes from non-associative algebras

Contact Info

Product

Resources

About

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