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Unique Decoding of Plane AG Codes Revisited [article]

Kwankyu Lee
2012 arXiv   pre-print
We reformulate a recently introduced interpolation-based unique decoding algorithm of algebraic geometry codes using the theory of Gr\"obner bases of modules on the coordinate ring of the base curve.  ...  With the same decoding performance, the new algorithm has a more conceptual description that lets us better understand the majority voting procedure central in the interpolation-based unique decoding.  ...  Introduction Recently a new kind of unique decoding algorithm of algebraic geometry codes appeared [2] .  ... 
arXiv:1204.0052v2 fatcat:ndta3h5mgbdrpk23usmaut6pma


Kwankyu Lee
2014 Journal of Applied Mathematics and Informatics  
We reformulate an interpolation-based unique decoding algorithm of AG codes, using the theory of Gröbner bases of modules on the coordinate ring of the base curve.  ...  The conceptual description of the reformulated algorithm lets us better understand the majority voting procedure, which is central in the interpolation-based unique decoding.  ...  Comparing with the well-known classical unique decoders of AG codes, Berlekamp-Massey-Sakata algorithm [7] and Kötter's algorithm [3] , the features of the new algorithm put it in a unique place in  ... 
doi:10.14317/jami.2014.083 fatcat:sxvwvwpw3rabjjutspsnxv3w4a

Algebraic aspects of two-dimensional convolutional codes

E. Fornasini, M.E. Valcher
1994 IEEE Transactions on Information Theory  
Two-dimensional (2D) codes are introduced as linear shift-invariant spaces of admissible signals on the discrete plane.  ...  The algebraic structure of the class of all encoders that correspond to a given convolutional code is investigated and the possibility of obtaining 2D decoders, free from catastrophic errors, as well as  ...  Most of the concepts introduced in the previous parts are revisited in the section devoted to the duality notion.  ... 
doi:10.1109/18.335967 fatcat:qb2dk5q4ivdodl2uop6ih3itwi

Attaining Sudan's decoding radius with no genus penalty for algebraic geometry codes [article]

Isabella Panaccione
2021 arXiv   pre-print
In this paper we present a decoding algorithm for algebraic geometry codes with error-correcting capacity beyond half the designed distance of the code.  ...  The decoding radius of this algorithm reaches that of Sudan algorithm, without any penalty given by the genus of the curve.  ...  Proposition 1.10 (Star product of AG codes).  ... 
arXiv:2103.11188v2 fatcat:apaorxwzsrc6rc75lnv4gnhytq

Revisiting silk: a lens-free optical physical unclonable function

Min Seok Kim, Gil Ju Lee, Jung Woo Leem, Seungho Choi, Young L. Kim, Young Min Song
2022 Nature Communications  
One emerging method for guaranteeing digital security is to take advantage of a physical unclonable function.  ...  AbstractFor modern security, devices, individuals, and communications require unprecedentedly unique identifiers and cryptographic keys.  ...  From the raw data, three unique planes are detected under light illumination of three colors (i.e., red, green, and blue) at different incident angles (i.e., −15°, 0°and +15°) (Fig. 1e ; (i)).  ... 
doi:10.1038/s41467-021-27278-5 pmid:35017474 pmcid:PMC8752800 fatcat:fhptwkvt6ffwdpl2ldlralyflu

Performance analysis of turbo-coded APSK modulations over nonlinear satellite channels

R. De Gaudenzi, A. Guillen i Fabregas, A. Martinez
2006 IEEE Transactions on Wireless Communications  
For the latter, a new class of non turbo decoder-aided closed-loop phase synchronizers featuring good performance and low complexity is studied.  ...  The effect of the satellite nonlinearity is studied, and distortion pre-and post-compensation techniques for coded APSK are presented.  ...  As for trellis coded modulation we used a third-order timing interpolator. If not specified, the number of decoding iterations is set to 10.  ... 
doi:10.1109/twc.2006.1687763 fatcat:buda7szugzgb7o57w2qd2mn4be

Fractal MapReduce decomposition of sequence alignment

Jonas S Almeida, Alexander Grüneberg, Wolfgang Maass, Susana Vinga
2012 Algorithms for Molecular Biology  
The dramatic fall in the cost of genomic sequencing, and the increasing convenience of distributed cloud computing resources, positions the MapReduce coding pattern as a cornerstone of scalable bioinformatics  ...  Conclusions: The procedure described is an attempt at extreme decomposition and parallelization of sequence alignment in anticipation of a volume of genomic sequence data that cannot be met by current  ...  to a unique [0, 1] n coordinate.  ... 
doi:10.1186/1748-7188-7-12 pmid:22551205 pmcid:PMC3394223 fatcat:uxlwxup4azfk3keelp7j55nqsi

Hybrid Attention for Automatic Segmentation of Whole Fetal Head in Prenatal Ultrasound Volumes [article]

Xin Yang, Xu Wang, Yi Wang, Haoran Dou, Shengli Li, Huaxuan Wen, Yi Lin, Pheng-Ann Heng, Dong Ni
2020 arXiv   pre-print
and Objective: Biometric measurements of fetal head are important indicators for maternal and fetal health monitoring during pregnancy. 3D ultrasound (US) has unique advantages over 2D scan in covering  ...  To enhance the spatial consistency in segmentation, we further organize multiple segmentors in a cascaded fashion to refine the results by revisiting context in the prediction of predecessors.  ...  Code is publicly available  ... 
arXiv:2004.13567v1 fatcat:u2mfb3zpbjc35amu6yw74g4q2e

Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial

Igal Sason, Shlomo Shamai
2006 Foundations and Trends in Communications and Information Theory  
The work was supported by the EU 6 th International Framework Programme via the NEWCOM Network of Excellence.  ...  Acknowledgments We are grateful to Idan Goldenberg, Gil Wiechman and Moshe Twitto for detecting typos and providing useful comments which improved the lucidity of the presentation.  ...  This was achieved by determining the region R as a boundary of a plane.  ... 
doi:10.1561/0100000009 fatcat:vtswtioifnccfan4i4f3pj5uj4

Spectral Reconstruction and Disparity from Spatio-Spectrally Coded Light Fields via Multi-Task Deep Learning [article]

Maximilian Schambach, Jiayang Shi, Michael Heizmann
2021 arXiv   pre-print
The results are compared to state-of-the art compressed sensing reconstruction and disparity estimation. We achieve a high reconstruction quality for both synthetic and real-world coded light fields.  ...  The disparity estimation quality is on par with or even outperforms state-of-the-art disparity estimation from uncoded RGB light fields.  ...  Coded Light Fields In the plane-plane parametrization, the spectral light field is denoted by L(u, v, s, t, λ), where (u, v) corresponds to the angular component of the light field, (s, t) to the spatial  ... 
arXiv:2103.10179v2 fatcat:lsflklagijhcfmaj74447eaq44

Geometric analogue of holographic reduced representation

Diederik Aerts, Marek Czachor, Bart De Moor
2009 Journal of Mathematical Psychology  
Geometric analogues of HRRs are obtained if one considers a projective representation of the same group in the space of blades (geometric products of basis vectors) associated with an arbitrary n-dimensional  ...  Restricting HRRs to n-tuples consisting of ±1, one reinterprets the variable binding as a representation of the additive group of binary n-tuples with addition modulo 2.  ...  Decoding of the 'name' looks as follows: Pat' = name ⊕ PSmith = name ⊕ (name ⊕ Pat) (sex ⊕ male) (age ⊕ 66) = Pat (name ⊕ sex ⊕ male) (name ⊕ age ⊕ 66) = Pat noise → Pat.  ... 
doi:10.1016/ fatcat:57df3xdcwzhszmzru3vxvsrxhy

Quantum Goppa Codes over Hyperelliptic Curves [article]

Annika Niehage
2005 arXiv   pre-print
This Diplom thesis provides an explicit construction of a quantum Goppa code for any hyperelliptic curve over a non-binary field. Hyperelliptic curves have conjugate pairs of rational places.  ...  Furthermore we present a projection of a higher dimensional code onto the base field and a special case when the projected code is again weighted self-orthogonal and symmetric.  ...  The CSS Construction Revisited This section shows how we can use hyperelliptic curves to construct quantum AG codes.  ... 
arXiv:quant-ph/0501074v1 fatcat:2eoxnuw7dzcphoafkgybmj6nzq

Machine Learning for Multimedia Communications

Nikolaos Thomos, Thomas Maugey, Laura Toni
2022 Sensors  
For example, the high model capacity of the learning-based architectures enables us to accurately model the image and video behavior such that tremendous compression gains can be achieved.  ...  However, learning-based algorithms often imply drastic changes to the way data are represented or consumed, meaning that the overall pipeline can be affected even though a subpart of it is optimized.  ...  The joint consideration of source and coding has been revisited to design systems that meet the expectations of future multimedia coding and communication systems.  ... 
doi:10.3390/s22030819 pmid:35161566 pmcid:PMC8840624 fatcat:nmz7s6ei3bdddarbt2bqhf6beu

A Multiplexed, Heterogeneous, and Adaptive Code for Navigation in Medial Entorhinal Cortex

Kiah Hardcastle, Niru Maheswaranathan, Surya Ganguli, Lisa M. Giocomo
2017 Neuron  
Combined, these observations advance our current understanding of the mechanistic origins and functional implications of the entorhinal code for navigation.  ...  This approach successfully classifies the majority of entorhinal cells and reveals unsuspected entorhinal coding principles.  ...  McDonnell Foundation, and an Office of Naval Research grant to SG, as well as an NSF-IGERT from the Stanford MBC Program and a Stanford Interdisciplinary Graduate Fellowship to KH.  ... 
doi:10.1016/j.neuron.2017.03.025 pmid:28392071 pmcid:PMC5498174 fatcat:wuwbir5bkrgk7fehqme6z4mmiu

Bounds on Separating Redundancy of Linear Codes and Rates of X-Codes [article]

Yu Tsunoda, Yuichiro Fujiwara, Hana Ando, Peter Vandendriessche
2016 arXiv   pre-print
While the two types of errors can be corrected simultaneously with error-correcting codes, it is also known that any linear code allows for first correcting errors and then erasures in two-step decoding  ...  This leads to an exponentially improved bound on the size of an optimal X-code.  ...  They revisited a classical strategy in which the decoder first corrects errors using the punctured code obtained by discarding the erased digits and then handles the erasures with the original linear code  ... 
arXiv:1609.03547v1 fatcat:khigi4ltmrcf7nliotqvkrtyai
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