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Spread Decoding in Extension Fields
[article]
2012
arXiv
pre-print
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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
2014
2014 IEEE International Symposium on Information Theory
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2014 pre-print arXiv:1401.0615v1 fatcat:r5unfskipfhuzaoi3fnce5v7ta
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
2012
Advances in Mathematics of Communications
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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
2010
2010 5th Advanced Satellite Multimedia Systems Conference and the 11th Signal Processing for Space Communications Workshop
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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]
2012
arXiv
pre-print
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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
2005
IEEE Transactions on Information Theory
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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]
2017
arXiv
pre-print
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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
2007
IEEE Journal of Selected Topics in Quantum Electronics
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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
2020
EURASIP Journal on Wireless Communications and Networking
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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
1985
Discrete Mathematics
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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
2020
Emerging Science Journal
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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
1988
Optics Letters
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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]
2016
arXiv
pre-print
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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
2012
International Journal of Computer Applications
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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
2017
Designs, Codes and Cryptography
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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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