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Spread Decoding in Extension Fields [article]

Felice Manganiello, Anna-Lena Trautmann
2012 arXiv   pre-print
It can be constructed in different ways which lead to different decoding algorithms.  ...  In this work we present a new representation of spread codes with a minimum distance decoding algorithm which is efficient when the codewords, the received space and the error space have small dimension  ...  In this work we translate this construction to an extension field setting and evolve a decoding algorithm for spread codes in this setting.  ... 
arXiv:1108.5881v2 fatcat:utoisnsbtzafja2h2ovbubndt4

Message encoding for spread and orbit codes

Anna-Lena Trautmann
2014 2014 IEEE International Symposium on Information Theory  
In this work we show how the message space can be chosen for a given code and how message en- and decoding can be done.  ...  Spread codes and orbit codes are special families of constant dimension subspace codes.  ...  In the isomorphic extension field representation, A maps the basis {1, β, β 2 , β 3 } of F q n over F q to the new basis {1, β + β 2 , 1 + β, β + β 3 }.  ... 
doi:10.1109/isit.2014.6875303 dblp:conf/isit/Trautmann14 fatcat:za6irvaegvhylkdu2biqk7rd2e

An algebraic approach for decoding spread codes

Elisa Gorla, Felice Manganiello, Joachim Rosenthal
2012 Advances in Mathematics of Communications  
We give a minimum-distance decoding algorithm which requires O((n−k)k3) operations over an extension field Fqk.  ...  In other words, the codewords are full-rank matrices of size k×n with entries in a finite field Fq. Spread codes are a family of optimal codes with maximal minimum distance.  ...  Acknowledgments The authors are grateful to Heide Gluesing-Luerssen for useful discussions and help in the proof of Theorem 25.  ... 
doi:10.3934/amc.2012.6.443 fatcat:rcmkygpyvrghjb5cqncw6ywbtm

Adding different levels of QoS to the DVB-SH standard

Aharon Vargas, Marco Breiling, Wolfgang H. Gerstacker, Holger Stadali, Ernst Eberlein, Albert Heuberger
2010 2010 5th Advanced Satellite Multimedia Systems Conference and the 11th Signal Processing for Space Communications Workshop  
An extension of the interleaving scheme is investigated to support low latency service requirements for interactive services based on short messages.  ...  The first approach is a straightforward extension of the DVB-SH interleaver scheme based on an early-uniform interleaver profile, and the second one is the introduction of a super short interleaver, referred  ...  Two of these solutions require an extension of the DVB-SH standard in order to provide an extra level of QoS.  ... 
doi:10.1109/asms-spsc.2010.5586882 fatcat:irejppnbizaeng3cx23wolddj4

An Algebraic Approach for Decoding Spread Codes [article]

Elisa Gorla and Felice Manganiello and Joachim Rosenthal
2012 arXiv   pre-print
We give a minimum-distance decoding algorithm which requires O((n-k)k^3) operations over an extension field F_q^k.  ...  In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family of optimal codes with maximal minimum distance.  ...  Acknowledgement The authors are grateful to Heide Gluesing-Luerssen for useful discussions and help in the proof of Theorem 25.  ... 
arXiv:1107.5523v4 fatcat:jyjnf4zyufhodbpvvxq2si4qva

Maximal Diversity Algebraic Space–Time Codes With Low Peak-to-Mean Power Ratio

P. Dayal, M.K. Varanasi
2005 IEEE Transactions on Information Theory  
With antennas and a rate of one symbol per channel use, the LPST codes lead to a decrease in PMEPR by at least a factor of relative to a Hadamard spread version of the TAST code.  ...  The LPST codes are obtained using the properties of certain cyclotomic number fields.  ...  A finite-dimensional algebraic extension of is known as an algebraic number field. will be referred to as the th conjugate of . • The algebraic number field is known as the th cyclotomic number field.  ... 
doi:10.1109/tit.2005.846398 fatcat:hbg2pjm4pjcazh5jdj3sw4ziea

Symbol Erasure Correction Capability of Spread Codes [article]

Heide Gluesing-Luerssen, Anna-Lena Horlemann-Trautmann
2017 arXiv   pre-print
Furthermore, we explain how to decode these codes in the two channel models and compare their decoding complexities.  ...  For both models we derive the symbol erasure correction capabilities of spread codes and compare them to other known codes suitable for those models.  ...  Overall, it depends on the importance of decoding speed and the field size in the given application if spread or hybrid codes are the better choice.  ... 
arXiv:1710.06323v1 fatcat:bk32vctpdrfk7n3phcki7x2u4q

80.8-km BOSSNET SPECTS O-CDMA Field Trial Using Subpicosecond Pulses and a Fully Integrated, Compact AWG-Based Encoder/Decoder

Ryan P. Scott, Vincent J. Hernandez, Nicolas K. Fontaine, Francisco M. Soares, Ronald Broeke, Kevin Perry, George Nowak, Chunxin Yang, Wei Cong, Katsunari Okamoto, Brian H. Kolner, Jonathan P. Heritage (+1 others)
2007 IEEE Journal of Selected Topics in Quantum Electronics  
A novel tunable dispersion-slope compensator enables the use of subpicosecond pulses without extensive characterization of the field-deployed fiber.  ...  We successfully demonstrate a spectral phaseencoded time-spreading (SPECTS) optical code-division multipleaccess (O-CDMA) field trial on an 80.8-km link within the Boston-South Network (BOSSNET) using  ...  Recently, alternative O-CDMA systems have been demonstrated in field trials; a 111-km field trial using spectral amplitude encoding [19] , a 50-km field trial of a direct time-spreading O-CDMA [20] ,  ... 
doi:10.1109/jstqe.2007.897649 fatcat:7dnm5yyhqrbwlgigfvi2a25d3q

Research on correction algorithm of propagation error in wireless sensor network coding

Dongqiu Zhang, Mingyong Pang, Guangzhi Zhang, Dandan Huang
2020 EURASIP Journal on Wireless Communications and Networking  
For random networks, changing their topologies over time, original errors can be spread to the down-stream nodes in the networks and cause the decoding failure when the Hamming metric is used.  ...  We combine a small field with rank-metric codes to solve this problem in this paper.  ...  Acknowledgements The authors acknowledged the anonymous reviewers and editors for their efforts in valuable comments and suggestions.  ... 
doi:10.1186/s13638-020-01733-1 fatcat:rfmamhxupjb6hgxfq7p4oubup4

An extension of the codes introduced by Séguin, allard and Bhargava

Bernard Courteau, Jean Goulet
1985 Discrete Mathematics  
A (I, q)-byte or simply a I-byte is a sequence of 1 s q* elements in the field GF(q). Let S = {Wi ) i E I} be a partial t-spread in GF(q)'.  ...  Define the (1 x 2) matrices Mj as follows: the first column of Mi is the zero vector and the other columns are a sequence of 1 -1 distinct non-zero vectors chosen in Wi.  ...  in the field F= GF(q(a-l)*+b).  ... 
doi:10.1016/0012-365x(85)90021-4 fatcat:pw4wbxnwqjafrm53j22lzomyjy

An Efficient Decoding Algorithm for Block Codes Based on the Communication Channel Reliability Information

Yong-Geol Shim
2020 Emerging Science Journal  
The algorithm finds out a group of candidate code words, in which the most likely one is chosen as a decoding result.  ...  For channel codes in communication systems, an efficient algorithm that controls error is proposed. It is an algorithm for soft decision decoding of block codes.  ...  Which decomposes into linear factors in some quadratic field (extension of the rational field of degree 2).  ... 
doi:10.28991/esj-2020-01235 fatcat:w2nu6xupw5cvloqu6l26qz4uwi

Encoding and decoding of femtosecond pulses

A. M. Weiner, J. P. Heritage, J. A. Salehi
1988 Optics Letters  
Spreading is accomplished by encoding pseudorandom binary phase codes onto the optical frequency spectrum. Subsequent decoding of the spectral phases restores the original pulse.  ...  We demonstrate the spreading of femtosecond optical pulses into picosecond-duration pseudonoise bursts.  ...  In this Letter we demonstrate frequency-domain encoding and decoding (in the time domain, spreading and despreading) of femtosecond optical pulses.  ... 
doi:10.1364/ol.13.000300 pmid:19745879 fatcat:wb4it3dydrdobipwaqrfwdsg4a

Message Encoding and Retrieval for Spread and Cyclic Orbit Codes [article]

Anna-Lena Horlemann-Trautmann
2016 arXiv   pre-print
Spread codes and cyclic orbit codes are special families of constant dimension subspace codes.  ...  In this work we show how a message set of consecutive integers can be encoded and retrieved for these two code families.  ...  ACKNOWLEDGMENT The author would like to thank Yuval Cassuto for his reference to enumerative coding, John Sheekey for his advice on Desarguesian spreads, and Margreta Kuijper for fruitful discussions and  ... 
arXiv:1409.0610v3 fatcat:6xkj6kwbfjevtfszai3eejhv5m

Performance Analysis of Spread Spectrum with Prime Codes in a Wireless System Over a fading Channel

Sreesha SBabu, K. Jayanthi
2012 International Journal of Computer Applications  
Spread spectrum technology has become the technology for commercial systems operating in both the licensed as well as in the unlicensed spectrum.  ...  The performance of FH-SS is analyzed in AWGN channel. Prime codes are so considered as the best among the other methods.  ...  Besides the binary number 0 and 1, there are additional unique elements in the extension field that denotes the variable a.  ... 
doi:10.5120/6159-8564 fatcat:avmgmk23yfhppfubbwdksjk3ku

Message encoding and retrieval for spread and cyclic orbit codes

Anna-Lena Horlemann-Trautmann
2017 Designs, Codes and Cryptography  
Spread codes and cyclic orbit codes are special families of constant dimension subspace codes.  ...  In this work we show how a message set of consecutive integers can be encoded and retrieved for these two code families.  ...  The same computations can naturally also be done in the extension field representation, using F n q ∼ = F q n .  ... 
doi:10.1007/s10623-017-0377-x fatcat:taubfpo3sfbu3ikcj5vql6muqa
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