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Chained Successive Cancellation Decoding of the Extended Golay code
[article]
2018
arXiv
pre-print
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The extended Golay code is shown to be representable as a chained polar subcode. This enables its decoding with the successive cancellation algorithm and its stack generalization. ...
The complexity of the obtained algorithm is comparable with that of the Vardy algorithm. ...
The standard way to construct polar codes is to let F be the set of low-capacity subchannels. However, the minimum distance of classical polar codes is quite low. ...
arXiv:1801.06315v1
fatcat:pruxtccv55gcrdfzy6tmmvd2me
Doppler Resilient Golay Complementary Waveforms
2008
IEEE Transactions on Information Theory
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We describe a method of constructing a sequence (pulse train) of phase-coded waveforms, for which the ambiguity function is free of range sidelobes along modest Doppler shifts. ...
The Prouhet-Thue-Morse sequence plays a key role in the construction of Doppler resilient sequences of Golay complementary waveforms. ...
Construction of low PMEPR codes from cosets of the generalized first-order Reed-Muller code has also been considered by Schmidt [26] and by Schmidt and Finger [27] . ...
doi:10.1109/tit.2008.928292
fatcat:cmtlyz4mavf7lov3fcgnzwbw3e
Composite QAM sequences with low PMEPR
2002
Electronics Letters
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At 4 GHz, the measured insertion loss was 0.5 dB for the capacitive path and 0.4 dB for the inductive path, with a differential phase shift of 9 I". ...
The transmitted signal in an OFDM system is then represented as: Construction of Golay (or Golay-like) sequences with low PMEPR bascd on RM codes is introduced for codewords of length 32 or less. ...
-K.: 'Meander-line polarizer for arbitrary rotation of linear polarization', IEEE Microw. Guide. ...
doi:10.1049/el:20020898
fatcat:h64nxt5pujbzjmnuvqdfmxybfu
Transformation of Binary Linear Block Codes to Polar Codes with Dynamic Frozen
2020
IEEE Open Journal of the Communications Society
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In this paper, a general transformation of binary linear block codes (BLBCs) to (possibly, multi-kernel) polar codes with dynamic frozen bits is proposed. ...
This transformation allows the usage of any decoding algorithm of polar codes for efficient soft decoding of BLBCs, including the powerful successive cancellation list (SCL) decoding algorithm. ...
SOFT POLAR DECODING OF BCH CODES, GOLAY CODES AND LDPC CODES In this section, we examine the proposed transformation and its respective polar decoding for BCH codes (Example 1), Golay codes (Example 2) ...
doi:10.1109/ojcoms.2020.2979529
fatcat:b3ohm5r2endzzmbvadkw7n6lha
On short-length error-correcting codes for 5G-NR
2018
Ad hoc networks
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The word error rate versus the signal-to-noise ratio is found for LDPC, Reed-Muller, Polar, Turbo, Golay, random, and BCH codes at length 20, 32 and 256 bits. ...
We use the probabilistic Ordered Statistics Decoder, that is universal to any code construction. As such we compare codes and not decoders. ...
Amira Alloum would like to thank her colleagues of 5G-NR RAN1 channel coding working group for the valuable discussions. ...
doi:10.1016/j.adhoc.2018.06.005
fatcat:2aibamtkxjcpdlwgrtqysrbk34
Coding to reduce both PAR and PICR of an OFDM signal
2002
IEEE Communications Letters
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As an example of an explicit construction for such codes, we construct Golay complementary repetition codes that can reduce both PAR and PICR simultaneously. ...
This paper shows the existence of codes to reduce both the PAR and PICR simultaneously. The coding scheme is based on selecting only those messages with both low PAR and PICR as valid codewords. ...
Golay Complementary Repetition Codes A simple approach to construct codes to reduce both PAR and PICR simultaneously is to use repetitive coding of Golay complementary sequence of length . ...
doi:10.1109/lcomm.2002.802065
fatcat:555gpkoerzao5osgkskvw7nm5q
Instantaneous Radar Polarimetry with Multiple Dually-polarized Antennas
2006
2006 Fortieth Asilomar Conference on Signals, Systems and Computers
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Alamouti signal processing is used to coordinate transmission of Golay pairs of phase codes waveforms across polarizations and multiple antennas. ...
Fully polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. ...
[3] employ Golay pairs of phase-coded waveforms [10] , [11] to provide synchronization and enable use of the Alamouti space-time code [12] to coordinate transmission of Golay pairs across polarizations ...
doi:10.1109/acssc.2006.354850
fatcat:qdeaci7bp5hojecavt6joxsa7u
Golay Layer: Limiting Peak-to-Average Power Ratio for OFDM-based Autoencoders
[article]
2020
arXiv
pre-print
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The proposed approach relies on the manipulation of the parameters of a set of functions that yield complementary sequences (CSs) through a deep neural network (DNN). ...
Numerical results show that DNNs at the transmitter and receiver can achieve reliable communications under this protection layer at the expense of complexity. ...
In this case, the performance of the OFDM with polar code is better than that of OFDM-AEs. ...
arXiv:2002.07701v1
fatcat:hlbm4jxzo5fm5ezqze4jojzwdy
Doppler Resilient Waveforms with Perfect Autocorrelation
[article]
2007
arXiv
pre-print
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We describe a method of constructing a sequence of phase coded waveforms with perfect autocorrelation in the presence of Doppler shift. ...
The Prouhet-Thue-Morse sequence plays a key role in the construction of Doppler resilient sequences of Golay pairs. ...
Construction of low PMEPR codes from cosets of the generalized first-order Reed-Muller code has also been considered by Schmidt [31] and Schmidt and Finger [32] . ...
arXiv:cs/0703057v1
fatcat:kcuxx5kh25fj3ebju7443tj3xa
Page 2299 of Mathematical Reviews Vol. , Issue 2002C
[page]
2002
Mathematical Reviews
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David, Jr.; Vardy, Alexander (1-IL-S; Urbana, IL) Classification of certain tail-biting generators for the binary Golay code. ...
The binary Golay code C4 and its symmetry group, the Mathieu group Mp4, are examined. ...
Unitary design of radar waveform diversity sets
2008
2008 42nd Asilomar Conference on Signals, Systems and Computers
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A 4×4 example involves two spatially separated antennas with each able to transmit and receive simultaneously on two different polarizations. ...
Perfect reconstruction means the sum of the time-autocorrelations associated with each of the four waveforms is a delta function. ...
We showed that Golay codes, Barker codes and quarter-band filters possess good separation properties and if we construct waveforms using a combination of these constituent waveforms through the use of ...
doi:10.1109/acssc.2008.5074353
fatcat:bl5bw6mtezeo5dfhnk5jhoanhi
Unitary Design of Radar Waveform Diversity Sets
[chapter]
2010
Handbook on Array Processing and Sensor Networks
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A 4×4 example involves two spatially separated antennas with each able to transmit and receive simultaneously on two different polarizations. ...
Perfect reconstruction means the sum of the time-autocorrelations associated with each of the four waveforms is a delta function. ...
We showed that Golay codes, Barker codes and quarter-band filters possess good separation properties and if we construct waveforms using a combination of these constituent waveforms through the use of ...
doi:10.1002/9780470487068.ch7
fatcat:5yfloq6hovdtlhzxxhxhotaeae
The symmetries of the tetrahedral Kummer surface in the Mathieu group M_24
[article]
2011
arXiv
pre-print
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2010 pre-print arXiv:1008.0954v2 fatcat:keh554ab4rh4nfqvtqnsrgsyzeOther Versions
We provide a method, based on Nikulin's lattice gluing techniques, which identifies the symplectic automorphisms of Kummer surfaces as permutation groups on 24 elements preserving the Golay code. ...
Kondo's lattice construction, which uses a different gluing technique from the one advocated here to rederive Mukai's results, is reviewed, and a slight generalisation is used to check the consistency ...
Matthias Schütt deserves our gratitude for a number of helpful comments. We thank the London Mathematical Society for a Scheme 4 Collaborative Small Grant. ...
arXiv:1008.0954v3
fatcat:5bbbl4euhjelrbhv7b7jtkvwm4
Waveform Diversity in Radar Signal Processing
2009
IEEE Signal Processing Magazine
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Sixty years ago, efforts by Marcel Golay to improve the sensitivity of far infrared spectrometry led to the discovery of pairs of complementary sequences. ...
Given a single scatterer in the far field of each of the transmitters, the transmitted signals arrive at the scatterer as plane waves, with a direction of arrival κ κ κ n and complex polarization vector ...
This work was supported in part by the National Science Foundation under Grant 0701226, the Department of the Navy, Office of Naval Research under Grant N00014-02-100398, and the Air Force Office of Scientific ...
doi:10.1109/msp.2008.930414
fatcat:dvzxkabpyvhljetp2aabws4g44
Page 4560 of Mathematical Reviews Vol. , Issue 95h
[page]
1995
Mathematical Reviews
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Parker— a nonassociative extension of a group of order 2 by the extended binary Golay code, and proceeded via construction of a different 2-local of M, an extension of a 2-group of order 27+!! ...
Of course the ternary Golay code is well known in the literature; I believe those for p = 5,7 are known but less celebrated. ...
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