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Probabilistic Analysis of Linear Programming Decoding

C. Daskalakis, A.G. Dimakis, R.M. Karp, M.J. Wainwright
2008 IEEE Transactions on Information Theory  
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes.  ...  Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in correcting a constant fraction of errors with high probability.  ...  The focus of this paper is the probabilistic analysis of linear programming (LP) decoding, a technique first introduced by Feldman et al.  ... 
doi:10.1109/tit.2008.926452 fatcat:pzhpoqy6sbfuzljsgqr26rrdpi

Cumulative subject index volumes 60–63

1984 Information and Control  
probabilistic dynamic logic, 63, 11 Decisions equivalence between DPDA and linear DPDA, with intermediate machine technique, 62, 26 trees, optimal, for symmetric Boolean functions, 62, 129 Decoding  ...  power of first-order programming logic, 60, 12 Messages buffers, characterization and axiomatiza- tion in linear temporal logic, 63, 88 Models 2-calculus, and domains, effectiveness analysis, 62  ... 
doi:10.1016/s0019-9958(84)80017-0 fatcat:cnws7odqjre33jn42n3t72h46y

Cumulative subject index volumes 40–43

1979 Information and Control  
fields, 41, 243 Principal components method, relation to coordinate-free eigenvalue analysis, 42, 38 Probabilistic strings in stochastic languages, maximal der- ivations for, 42, 290 Processes  ...  investigation, 43, 50 Pushdown store automata realtime, and linear languages, 42, 27 Q Quasi-Optimizer program performance, power of heurist- ic rules in assessment, 40, 1 Queries order two,  ... 
doi:10.1016/s0019-9958(79)90069-x fatcat:prorkxke6ncuzeb52kxef5whba

Neural Decoding of Cursor Motion Using a Kalman Filter

Wei Wu, Michael J. Black, Yun Gao, Elie Bienenstock, Mijail Serruya, A. Shaikhouni, John P. Donoghue
2002 Neural Information Processing Systems  
Encoding and decoding of the neural data is achieved with a Kalman filter which has a number of advantages over previous linear filtering techniques.  ...  In contrast to previous work, we develop a control-theoretic approach that explicitly models the motion of the hand and the probabilistic relationship between this motion and the mean firing rates of the  ...  This work was supported in part by: the DARPA Brain Machine Interface Program, NINDS Neural Prosthetics Program and Grant #NS25074, and the National Science Foundation (ITR Program award #0113679).  ... 
dblp:conf/nips/WuBGBSSD02 fatcat:3uzqyuktzfepdjhflbhey2qz34

Iterative weighted ℓ1 Optimization for compressed sensing and coding

M. Amin Khajehnejad, Alexandros G. Dimakis, Babak Hassibi
2010 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers  
We introduce a novel algorithm for decoding binary linear codes by linear programming.  ...  We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the objective function based on the outcome of the original  ...  INTRODUCTION Linear programming (LP) decoding for binary linear codes was introduced by Feldman, Karger and Wainwright [2] .  ... 
doi:10.1109/acssc.2010.5757668 fatcat:wpz7ipptojhf7pxygue6vqgssi

Reweighted LP decoding for LDPC codes

M. Amin Khajehnejad, Alexandros G. Dimakis, Babak Hassibi, William Bradley
2010 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
We introduce a novel algorithm for decoding binary linear codes by linear programming.  ...  We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the objective function based on the outcome of the original  ...  BACKGROUND In this section, we will review the problem of linear programming decoding for linear codes.  ... 
doi:10.1109/allerton.2010.5706905 fatcat:igtsogw4orhivm3l27gkshxfay

Modeling and Decoding Motor Cortical Activity Using a Switching Kalman Filter

W. Wu, M.J. Black, D. Mumford, Y. Gao, E. Bienenstock, J.P. Donoghue
2004 IEEE Transactions on Biomedical Engineering  
Firing rates are modeled as a Gaussian mixture where the mean of each Gaussian component is a linear function of hand kinematics.  ...  The model generalizes previous encoding and decoding methods, addresses the non-Gaussian nature of firing rates, and can cope with crudely sorted neural data common in on-line prosthetic applications.  ...  The approach extends the observation model of the Kalman filter as a probabilistic mixture of linear Gaussian models.  ... 
doi:10.1109/tbme.2004.826666 pmid:15188861 fatcat:4h7wnvmg3fdmze7vk2z4k4a3je

Decoding Output Sequences for Discrete-Time Linear Hybrid Systems

Monal Narasimhamurthy, Sriram Sankaranarayanan
2022 25th ACM International Conference on Hybrid Systems: Computation and Control  
The decoding problem is NP-complete, and can be reduced to solving a mixed-integer linear program (MILP).  ...  In particular, once a sequence of modes/transitions is fixed, the problem of "filling in" the continuous states is performed by a linear programming problem.  ...  All opinions are those of the author and not necessarily of NSF.  ... 
doi:10.1145/3501710.3519530 fatcat:w7r432vsmrcufpz6hrxwsuhnlu

ToPS: A Framework to Manipulate Probabilistic Models of Sequence Data

André Yoshiaki Kashiwabara, Ígor Bonadio, Vitor Onuchic, Felipe Amado, Rafael Mathias, Alan Mitchell Durham, Hilmar Lapp
2013 PLoS Computational Biology  
The framework includes functionality for training, simulation and decoding of the models.  ...  In particular the framework provides a novel, flexible, implementation of decoding in GHMMs that detects when the architecture can be traversed efficiently.  ...  Acknowledgments The authors are indebted to Elias de Moraes Fernandes for the design of the ToPS logo. Author Contributions  ... 
doi:10.1371/journal.pcbi.1003234 pmid:24098098 pmcid:PMC3789777 fatcat:ljrheqixwfcexcvx7fp5kxzmki

LP decodable permutation codes based on linearly constrained permutation matrices

Tadashi Wadayama, Manabu Hagiwara
2011 2011 IEEE International Symposium on Information Theory Proceedings  
Making use of linear constraints imposed on the permutation matrices, we can formulate a soft-decoding problem for the proposed class of permutation codes as a linear programming (LP) problem.  ...  Two types of linear constraints are discussed; one is structured constraints and another is random constraints.  ...  Han Vinck for directing the author's attention to the field of permutation codes. The first author also wishes to thank Dr. Jun Muramatsu for inspiring discussions on permutations.  ... 
doi:10.1109/isit.2011.6033769 dblp:conf/isit/WadayamaH11 fatcat:u6ixobddsvd6bownlxrmnsluiy

LP-Decodable Permutation Codes Based on Linearly Constrained Permutation Matrices

Tadashi Wadayama, Manabu Hagiwara
2012 IEEE Transactions on Information Theory  
Making use of linear constraints imposed on the permutation matrices, we can formulate a soft-decoding problem for the proposed class of permutation codes as a linear programming (LP) problem.  ...  Two types of linear constraints are discussed; one is structured constraints and another is random constraints.  ...  Han Vinck for directing the author's attention to the field of permutation codes. The first author also wishes to thank Dr. Jun Muramatsu for inspiring discussions on permutations.  ... 
doi:10.1109/tit.2012.2196253 fatcat:glyeiowllfekhjk4a3jusdlymu

Reweighted LP Decoding for LDPC Codes

Amin Khajehnejad, Alexandros G. Dimakis, Babak Hassibi, Benjamin Vigoda, William Bradley
2012 IEEE Transactions on Information Theory  
We introduce a novel algorithm for decoding binary linear codes by linear programming.  ...  The method is based on solving a linear-programming relaxation of the integer program corresponding to the maximum likelihood (ML) decoding problem.  ...  This simple observation helps us extend the probabilistic analysis of [15] to robustness results for LP decoding.  ... 
doi:10.1109/tit.2012.2202211 fatcat:xergtyez5zakxjifa7n4rkuquq

Reweighted LP Decoding for LDPC Codes [article]

Amin Khajehnejad, Alexandros G. Dimakis, Babak Hassibi, Benjamin Vigoda, William Bradley
2011 arXiv   pre-print
We introduce a novel algorithm for decoding binary linear codes by linear programming.  ...  We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the objective function based on the outcome of the original  ...  This simple observation helps us extend the probabilistic analysis of [15] to robustness results for LP decoding.  ... 
arXiv:1103.2837v1 fatcat:koswmom43zdvbddb5aqjwlsupa

Cortical decoding of individual finger and wrist kinematics for an upper-limb neuroprosthesis

V. Aggarwal, F. Tenore, S. Acharya, M.H. Schieber, N.V. Thakor
2009 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society  
However, decoding the kinematics of fine motor movements, such as the manipulation of individual fingers, has not been demonstrated.  ...  Both linear and non-linear filters were designed to simultaneously predict kinematics of each digit and the wrist, and their performance compared using mean squared error and correlation coefficients.  ...  and Engineering Research Council of Canada (NSERC), and by NIH R01/R37 NS27686.  ... 
doi:10.1109/iembs.2009.5334129 pmid:19964645 pmcid:PMC2875998 fatcat:cf6frpnbkjhw5kshj2dbfnocsy

Local-Optimality Guarantees for Optimal Decoding Based on Paths [article]

Guy Even, Nissim Halabi
2012 arXiv   pre-print
Local-optimality implies both unique maximum-likelihood (ML) optimality and unique linear-programming (LP) decoding optimality.  ...  This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs.  ...  Analysis of Repeat-Accumulate Codes via Local-Optimality Feldman and Karger [FK02, FK04] introduced the concept of linear-programming based decoding for repeat-accumulate RA(q) turbo-like codes.  ... 
arXiv:1203.1854v2 fatcat:tulfwhpf4rfbdjdchhb362mmba
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