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The nonassociative algebras used to build fast-decodable space-time block codes

Susanne Pumplün, Andrew Steele
2015 Advances in Mathematics of Communications  
We present conditions for the algebras to be division and propose a construction for fully diverse fast decodable space-time block codes of rate-m for nm transmit and m receive antennas.  ...  Two of these families appear either explicitly or implicitly in the designs of fast-decodable space-time block codes in papers by Srinath, Rajan, Markin, Oggier, and the authors.  ...  Natarajan for allowing us to include Lemma 19.  ... 
doi:10.3934/amc.2015.9.449 fatcat:q25stfcrpvbj7addyph3z7uuwa

Fast-decodable MIDO codes from non-associative algebras

S. Pumplün, A. Steele
2015 International Journal of Information and Coding Theory  
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.  ...  Acknowledgments We would like to thank B. Sundar Rajan (Senior Member, IEEE) and L. P. Natarajan for providing us with Section 7 and the simulations.  ... 
doi:10.1504/ijicot.2015.068695 fatcat:6qmtux5ffrba5i32lfyro3diy4

Tensor products of nonassociative cyclic algebras [article]

Susanne Pumpluen
2015 arXiv   pre-print
Applications to space-time block coding are discussed.  ...  We study the tensor product of an associative and a nonassociative cyclic algebra.  ...  Applications to space-time block coding Space-time block codes are used for reliable high rate transmission over wireless digital channels with multiple antennas transmitting and receiving the data.  ... 
arXiv:1504.00194v2 fatcat:4r7w2vcrizbnfl2xmixid473o4

Tensor products of nonassociative cyclic algebras

S. Pumplün
2016 Journal of Algebra  
Applications to space-time block coding are discussed.  ...  We study the tensor product of an associative and a nonassociative cyclic algebra.  ...  Applications to space-time block coding Space-time block codes are used for reliable high rate transmission over wireless digital channels with multiple antennas transmitting and receiving the data.  ... 
doi:10.1016/j.jalgebra.2015.12.007 fatcat:j7xnywgy3berpmwfk3pups4ppe

Quotients of orders in algebras obtained from skew polynomials with applications to coding theory

Susanne Pumplün
2018 Communications in Algebra  
These natural orders have already been used to systematically construct fully diverse fast-decodable space-time block codes.  ...  We show how the quotients of natural orders can be employed for coset coding.  ...  The algebras (D, σ, d) with d ∈ L × or d ∈ F × are used to construct fast-decodable space-time block codes, the matrix representing their right multiplication with entries in K, i.e. computed with respect  ... 
doi:10.1080/00927872.2018.1461882 fatcat:nh5ktoefvnbqhedtbgmop3g64q

Quotients of orders in algebras obtained from skew polynomials with applications to coding theory [article]

Susanne Pumpluen
2018 arXiv   pre-print
These natural orders have already been used to systematically construct fully diverse fast-decodable space-time block codes.  ...  We show how the quotients of natural orders can be employed for coset coding.  ...  The algebras (D, σ, d) with d ∈ L × or d ∈ F × are used to construct fast-decodable space-time block codes, the matrix representing their right multiplication with entries in K, i.e. computed with respect  ... 
arXiv:1609.04201v2 fatcat:okbthy2xu5eotpwkt6ttl2fzwq

How to obtain division algebras used for fast-decodable space-time block codes

Susanne Pumplün
2014 Advances in Mathematics of Communications  
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 look at algebras (and codes) obtained from variations of this method.  ...  Central simple associative division algebras over number fields, in particular cyclic division algebras, have been used highly successfully to systematically build space-time block codes (cf. for instance  ... 
doi:10.3934/amc.2014.8.323 fatcat:g5q2j77jvvgl5b3sbm44ega4ay

Editorial

2020 Glasgow Mathematical Journal  
Some axiomatic approaches to VOAs inspired the introduction of code algebras.  ...  They are important in the study of symmetric spaces and their generalisations.  ...  Acknowledgements The organisers would like to thank the London Mathematical Society and the Heilbronn Institute for providing funding to support the workshop, and the Glasgow Mathematical Journal Trust  ... 
doi:10.1017/s0017089520000518 fatcat:6ub63vkv6zexdje4wyuouuonnq

How to obtain lattices from $$(f,\sigma ,\delta )$$ ( f , σ , δ ) -codes via a generalization of Construction A

S. Pumplün
2017 Applicable Algebra in Engineering, Communication and Computing  
We show how cyclic ( f, σ, δ)-codes over finite rings canonically induce a Zlattice in R N by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f .  ...  It has the potential to be applied to coset coding, in particular to wire-tap coding. Previous results by Ducoat and Oggier are obtained as special cases.  ...  Due to their large nuclei, the algebras S f were also successfully employed to systematically build fast-decodable fully diverse space-time block codes in [37, 48, 54] , see [49] , which are used for  ... 
doi:10.1007/s00200-017-0344-9 fatcat:rxf2r66qybce5j374dck2g3744

How to obtain lattices from (f,sigma,delta)-codes via a generalization of Construction A [article]

Susanne Pumpluen
2017 arXiv   pre-print
We show how cyclic (f,σ,δ)-codes over finite rings canonically induce a Z-lattice in R^N by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f.  ...  It has the potential to be applied to coset coding, in particular to wire-tap coding. Previous results by Ducoat and Oggier are obtained as special cases.  ...  Due to their large nuclei, the algebras S f were also successfully employed to systematically build fast-decodable fully diverse space-time block codes in [51, 57, 39] , see [52] , which are used for  ... 
arXiv:1607.03787v2 fatcat:hd62y7okkfcqzd74azx4h3ohnq

A software-defined communications baseband design

J. Glossner, D. Iancu, Jin Lu, E. Hokenek, M. Moudgill
2003 IEEE Communications Magazine  
Software Defined Radios (SDRs) offer a programmable and dynamically reconfigurable method of reusing hardware to implement the physical layer processing of multiple communications systems.  ...  Our solution is programmed in C and executed on a multithreaded processor in real-time.  ...  The compiler uses this information to group highly traversed paths into larger blocks of code which can then be optimized and parallelized.  ... 
doi:10.1109/mcom.2003.1166669 fatcat:ulgis2pdhzd3niw2vwvc3p5spa

Impact of high-level transformations within the ROCCC framework

Betul Buyukkurt, John Cortes, Jason Villarreal, Walid A. Najjar
2010 ACM Transactions on Architecture and Code Optimization (TACO)  
computation in space by a circuit rather than in time by a sequence of instructions.  ...  generated from unoptimized codes, (3) loop-level optimizations to increase the throughput, and (4) transformations unique to certain classes of applications.  ...  The ROCCC compiler builds and pipelines the data path ] from the scalar replaced code.  ... 
doi:10.1145/1880043.1880044 fatcat:7xolpnbyk5ccddbsxyytyl5sxi

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
codes 94B27 Geometric methods (including applications of algebraic geometry) [See also 11T71, 14G50] 94B30 Majority codes 94B35 Decoding 94B40 Arithmetic codes [See also 11T71, 14G50] 94B50  ...  Ideally, the MSC codes attached to an item should represent the subjects to which the item contains a contribution.  ...  geometry [See also 58B34] 83C75 Space-time singularities, cosmic censorship, etc. 83C80 Analogues in lower dimensions 83C99 None of the above, but in this section 83Dxx Relativistic gravitational theories  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

Rendering and Visualization in Affordable Parallel Environments [article]

Dirk Bartz, Claudio Silva, Bengt-Olaf Schneider
1998 Eurographics State of the Art Reports  
-, object-, and time- space parallelism).  ...  The current technology push in the consumer market for graphics hardware, small multiprocessor machines, and fast networks is bound to make all of these components less expensive.  ...  We thank Tzicker Chiueh, Pat Crossno, Steve Dawson, Juliana Freire, Ron Peierls, and Amitabh Varshney for useful discussions about the PVR system and for help with this paper.  ... 
doi:10.2312/egt.19981025 fatcat:axdwegaosfbufdximddrntledq

CORPORATE CONTRIBUTORS

1988 The Hastings center report  
Next we used spike-time-dependent plasticity to optimize the prediction filters at both the spike-generator and decoder.  ...  RETINAL ADAPTATION TO SPACE-TIME CORRELATIONS.  ...  The network consists of 3 main parts: bilateral VMPFC which provides familiarity/context information that is used to select the appropriate transformation (Adolphs et al., 1996) ; left language areas  ... 
doi:10.1002/j.1552-146x.1988.tb03932.x fatcat:bkotcyah2ngbfdk4kbx3xnf5v4
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