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Performance Evaluation of Finite Sparse Signals for Compressed Sensing Frameworks

Jin-Taek SEONG
2018 IEICE transactions on information and systems  
In this paper, we consider to develop a recovery algorithm of a sparse signal for a compressed sensing (CS) framework over finite fields.  ...  We compare our simulation results with the theoretic bounds obtained from probability analysis. key words: compressed sensing, finite fields, signal recovery, probabilistic decoding  ...  In [7] , the authors have proposed a sparse recovery framework with sparse random network transfer matrices over finite fields to solve the network coding problems.  ... 
doi:10.1587/transinf.2017edl8166 fatcat:ezex4wxt5bcjbg3mhw7yqi7g7i

On Finite Alphabet Compressive Sensing [article]

Abhik Kumar Das, Sriram Vishwanath
2013 arXiv   pre-print
This paper considers the problem of compressive sensing over a finite alphabet, where the finite alphabet may be inherent to the nature of the data or a result of quantization.  ...  designs of sensing matrices based on coding-theoretic techniques; (c) enable one to solve the exact ℓ_0-minimization problem in polynomial time rather than a approach of convex relaxation followed by  ...  For example, finding the logarithm is a simple inversion for real values but NP-hard over finite fields.  ... 
arXiv:1303.3943v1 fatcat:obmxdfmzkbaspozmzrukq7oyje

The Hardness of LPN over Any Integer Ring and Field for PCG Applications [article]

Hanlin Liu, Xiao Wang, Kang Yang, Yu Yu
2022 IACR Cryptology ePrint Archive  
Although existing protocols based on LPN over integer rings use parameters as if they are over finite fields, we found an attack that effectively reduces the weight of a noise by half compared to LPN over  ...  We show that even after bringing all classical LPN cryptanalysis to the setting over finite fields, much less weight of noises is needed for the same level of security.  ...  b = A • s + e) over a finite field F from random samples (A, u).  ... 
dblp:journals/iacr/LiuWYY22 fatcat:eegcvgbgerhhfnvtbg4itdjv5m

Efficient data compression from statistical physics of codes over finite fields

A. Braunstein, F. Kayhan, R. Zecchina
2011 Physical Review E  
In this paper we discuss a novel data compression technique for binary symmetric sources based on the cavity method over a Galois Field of order q (GF(q)).  ...  The compression step is based on a reduction of sparse low density parity check codes over GF(q) and is done through the so called reinforced belief-propagation equations.  ...  Acknowledgment The authors wish to thank Guido Montorsi and Abolfazl Ramezanpour for valuable suggestions and useful discussions. RZ acknowledges the ERC grant OPTINF 267915.  ... 
doi:10.1103/physreve.84.051111 pmid:22181373 fatcat:2pheajtygvfpvp5a7v6h7kczvq

Page 5343 of Mathematical Reviews Vol. , Issue 84m [page]

1984 Mathematical Reviews  
The authors present a new approach to obtain cyclic convolution bilinear algorithms over the finite fields GF( p”), where p is a prime.  ...  His interest is in a rather elementary decoding algorithm based on the combinatorial properties of the parity-check matrix.  ... 

A Compressed Sensing-Based Low-Density Parity-Check Real-Number Code

Zaixing He, Takahiro Ogawa, Miki Haseyama, Xinyue Zhao, Shuyou Zhang
2013 Radioengineering  
A compressed sensing algorithm, Cross Low-dimensional Pursuit, is used to decode the code by solving this compressed sensing problem.  ...  In this paper, we propose a novel low-density parity-check real-number code, based on compressed sensing.  ...  Acknowledgements This research was supported by the Fundamental Research Funds for the Central Universities and Zhejiang Provincial Natural Science Foundation of China (LQ13F020002 and LQ13F030003).  ... 
doaj:4fcc11ccdfd84d2eb67e2997645f6438 fatcat:s7sygvy5szhkbltx5dubyaxrey

Page 8900 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
(I-MILANP-EI; Milan); Viola, Carlo (I-PISA; Pisa) Randomized algorithms over finite fields for the exact parity base problem.  ...  Algorithms 13 (1992), no. 2, 258-273; MR 93c:68034], use fast arithmetic work- ing over a finite field chosen at random among a set of appropriate fields.  ... 

Modulation-Function-Based Finite-Horizon Sensor Fault Detection for Salient-Pole PMSM using Parity-Space Residuals

Benjamin Jahn, Yuri A.W. Shardt
2021 IFAC-PapersOnLine  
An online model-based fault detection and isolation method for salient-pole permanent magnet synchronous motors over a finite horizon is proposed.  ...  The proposed approach combines parity-space-based residual generation and modulation-function-based filtering.  ...  Thus, this paper proposes a modulation-function-based approach to residual generation resulting in a residual signal evaluated over a finite horizon for sensor fault detection.  ... 
doi:10.1016/j.ifacol.2021.08.335 fatcat:liqi6c7irrhs3jbchgp7343upa

Geo Security using GPT Cryptosystem

Eraj Khan, Abbas Khalid, Arshad Ali, Muhammad Atif, Ahmad Salman
2020 International Journal of Advanced Computer Science and Applications  
In any code based cryptosystem, public and private keys are in the form of matrices based over the finite field.  ...  This work proposes an algorithm for calculating public and private key matrices based on the geographic location of the intended receiver.  ...  Let and represent a finite base field of q elements and an extension field of degree N respectively.  ... 
doi:10.14569/ijacsa.2020.0110265 fatcat:xm4ooxhbq5danl34ae6hf7y7qi

Optimization of NB QC-LDPC Block Codes and Their Performance Analysis [article]

Irina E. Bocharova, Boris D. Kudryashov, Evgenii P. Ovsyannikov, Vitaly Skachek, Tähvend Uustalu
2020 arXiv   pre-print
Tightened random coding bounds based on the average binary spectra for ensembles of "almost regular" NB LDPC codes of finite lengths over extensions of the binary Galois field are derived.  ...  This approach combines constructing of base parity-check matrices by simulated annealing and labeling the obtained base matrices aimed at maximizing the so-called generalized girth of the NB LDPC code  ...  The authors wish to thank Victor Krachkovsky, Oleg Kurmaev, Alexey Mayevskiy and Hongchen Yu for helpful discussions.  ... 
arXiv:2006.12147v2 fatcat:uwnc4xodfzho3hijutavaaesca

Worst configurations (instantons) for Compressed Sensing over reals: A channel coding approach

Shashi Kiran Chilappagari, Michael Chertkov, Bane Vasic
2010 2010 IEEE International Symposium on Information Theory  
We consider the Linear Programming (LP) solution of the Compressed Sensing (CS) problem over reals, also known as the Basis Pursuit (BasP) algorithm.  ...  We also prove that, given a sufficiently dense random input for the error-vector, the CS-ISA converges to an instanton in a small finite number of steps.  ...  This aspect of the CS is reminiscent of similar problem in the so-called expander graph based analysis [6] of the Low-Density Parity-Check (LDPC) codes [7] .  ... 
doi:10.1109/isit.2010.5513360 dblp:conf/isit/ChilappagariCV10 fatcat:slg5n4qtczarpkstby6ruvt5ui

Families of Optimal Binary Non-MDS Erasure Codes [article]

Danilo Gligoroski, Katina Kralevska
2016 arXiv   pre-print
but in the higher finite field GF(4).  ...  We introduce a definition for Families of Optimal Binary Non-MDS Erasure Codes for [n, k] codes over GF(2), and propose an algorithm for finding those families by using hill climbing techniques over Balanced  ...  Jensen for their discussions that improved the quality of this paper. We would also like to thank the anonymous reviewers for their useful comments and suggestions.  ... 
arXiv:1609.02460v1 fatcat:ptjs3igoqfg6jmpyuqwx7xiiju

Sub-Task Decomposition Enables Learning in Sequence to Sequence Tasks [article]

Noam Wies, Yoav Levine, Amnon Shashua
2022 arXiv   pre-print
An effective mitigation is to introduce intermediate supervision for solving sub-tasks of the compounded problem.  ...  The field of Natural Language Processing has experienced a dramatic leap in capabilities with the recent introduction of huge Language Models.  ...  Acknowledgments and Disclosure of Funding We thank Eran Malach and Shai Shalev-Shwartz for a helpful discussion on our stronger negative results, as well as Lifu Wang for clarifying Wang et al. (2021).  ... 
arXiv:2204.02892v2 fatcat:7cdnjyiarrcvredxzr5mjpwrlq

Code based Cryptography: Classic McEliece [article]

Harshdeep Singh
2020 arXiv   pre-print
We discuss the hard problems of coding theory which are used in code based cryptography and some classic attacks on it like information-set decoding (ISD).  ...  Successful implementation of the ISD attack on McEliece cryptosystem for some small parameters set is executed and the code for the same is provided in the Appendix.  ...  These problems were proved to be NP-complete in 1978 by Berlekamp et al. [7] for binary codes and in 1997 by Alexander Barg [2] for codes over all finite fields.  ... 
arXiv:1907.12754v2 fatcat:gt4rleeorba6zjtvol6qmwfyle

Applied Erasure Coding in Networks and Distributed Storage [article]

Katina Kralevska
2018 arXiv   pre-print
The demand for new ultra-fast and highly reliable coding techniques for data at rest and for data in transit is a major research challenge.  ...  The present thesis investigates efficient constructions of erasure codes for different applications.  ...  Recoding can be performed exclusively over the inner code in GF (2). Encoding and decoding is performed over the outer code in big finite fields.  ... 
arXiv:1803.01358v1 fatcat:ooellwzlkzekxdhm75snjpeggu
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