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List decoding algorithms for certain concatenated codes

Venkatesan Guruswami, Madhu Sudan
2000 Proceedings of the thirty-second annual ACM symposium on Theory of computing - STOC '00  
We give efficient (polynomial-time) list-decoding algorithms for certain families of error-correcting codes obtained by "concatenation".  ...  Specifically, we give list-decoding algorithms for codes where the "outer code" is a Reed-Solomon or Algebraic-geometric code and the "inner code" is a Hadamard code.  ...  All codes for which we give efficient list decoding algorithms from high noise are based on the idea of code concatenation.  ... 
doi:10.1145/335305.335327 dblp:conf/stoc/GuruswamiS00 fatcat:fxw6hucctval3la7nrjf25fz2q

List Decoding of Binary Codes–A Brief Survey of Some Recent Results [chapter]

Venkatesan Guruswami
2009 Lecture Notes in Computer Science  
We briefly survey some recent progress on list decoding algorithms for binary codes.  ...  The results discussed include: -Algorithms to list decode binary Reed-Muller codes of any order up to the minimum distance, generalizing the classical Goldreich-Levin algorithm for RM codes of order 1  ...  The improvement in [9] is based on using the Parvaresh-Vardy codes, which have better list-decoding guarantees, for the outer encoding.  ... 
doi:10.1007/978-3-642-01877-0_10 fatcat:35sc5keziffd5pu2qbmjeug2ja

Better Binary List-Decodable Codes Via Multilevel Concatenation [chapter]

Venkatesan Guruswami, Atri Rudra
2007 Lecture Notes in Computer Science  
A "level-by-level" decoding algorithm, which crucially uses the list recovery algorithm for folded Reed-Solomon codes from [8], enables list decoding up to the designed distance bound, aka the Blokh-Zyablov  ...  A probabilistic argument, which is also derandomized via conditional expectations, is used to show the existence of inner codes with a certain nested list decodability property that is appropriate for  ...  What makes this part more interesting than the usual code concatenation, is that the inner code in addition to having list decodable properties, also needs to have good list decodable properties for certain  ... 
doi:10.1007/978-3-540-74208-1_40 fatcat:iyydawrmunbivfa67yfslzyaqa

Better Binary List Decodable Codes Via Multilevel Concatenation

Venkatesan Guruswami, Atri Rudra
2009 IEEE Transactions on Information Theory  
A "level-by-level" decoding algorithm, which crucially uses the list recovery algorithm for folded Reed-Solomon codes from [8], enables list decoding up to the designed distance bound, aka the Blokh-Zyablov  ...  A probabilistic argument, which is also derandomized via conditional expectations, is used to show the existence of inner codes with a certain nested list decodability property that is appropriate for  ...  What makes this part more interesting than the usual code concatenation, is that the inner code in addition to having list decodable properties, also needs to have good list decodable properties for certain  ... 
doi:10.1109/tit.2008.2008124 fatcat:nly7b7jwx5gp3kudrmc7bqvusm

On the Construction and Decoding of Concatenated Polar Codes [article]

Hessam Mahdavifar, Mostafa El-Khamy, Jungwon Lee, Inyup Kang
2013 arXiv   pre-print
We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity.  ...  A scheme for concatenating the recently invented polar codes with interleaved block codes is considered.  ...  Further improved decoding algorithms for polar codes as CRC-aided list decoding [13] have the potential to improve the performance of the proposed successive decoding of concatenated polar codes.  ... 
arXiv:1301.7491v1 fatcat:dy7koswl5fadvbl5wsik5j6uxu

Quantum List Decoding of Classical Block Codes of Polynomially Small Rate from Quantumly Corrupted Codewords [article]

Tomoyuki Yamakami
2016 arXiv   pre-print
However, the code rates of all known families of efficiently quantum list-decodable codes are, unfortunately, too small for other practical applications.  ...  As an immediate application, we use the quantum list decodability of this code family to solve a certain form of quantum search problems in polynomial time.  ...  Acknowledgments The author thanks Akinori Kawachi for a discussion on quantum cryptography and Igor Shparlinski for a useful pointer to Reference (Bleichenbacher and Nguyen [3] ) when the author was preparing  ... 
arXiv:quant-ph/0610200v4 fatcat:4opddrjbxrbapbaaw4vzvxzdqy

Quantum List Decoding of Classical Block Codes of Polynomially Small Rate from Quantumly Corrupted Codewords

Tomoyuki Yamakami
2016 Baltic Journal of Modern Computing  
However, the code rates of all known families of efficiently quantum list-decodable codes are, unfortunately, too small for other practical applications.  ...  Moreover, assuming that NP BQP, we also prove that no efficient quantum list decoder exists for the generalized Reed-Solomon codes.  ...  Acknowledgments The author thanks Akinori Kawachi for a discussion on quantum cryptography and Igor Shparlinski for a useful pointer to Reference (Bleichenbacher and Nguyen, 2000) when the author was  ... 
doi:10.22364/bjmc.2016.4.4.12 fatcat:746pd32ixngrzi5i345ovpphg4

Timing Attack Resilient Decoding Algorithms for Physical Unclonable Functions [article]

Sven Puchinger and Sven Müelich and Antonia Wachter-Zeh and Martin Bossert
2016 arXiv   pre-print
This paper deals with the application of list decoding of Reed--Solomon codes to a concatenated code for key reproduction using Physical Unclonable Functions.  ...  We also show that their decoding algorithms can be protected from side-channel attacks on the runtime both by masking techniques and by directly modifying the algorithms to have constant runtime.  ...  ACKNOWLEDGEMENT We would like to thank Matthias Hiller and Vincent Immler for the valuable discussions and helpful comments on an earlier version of the paper.  ... 
arXiv:1611.07702v1 fatcat:aoykldyhpfavxfjjzkh5hykhoi

An efficient length- and rate-preserving concatenation of polar and repetition codes [article]

Mathis Seidl, Johannes B. Huber
2013 arXiv   pre-print
Decoding of the scheme integrates easily in the known successive decoding algorithms for polar codes. Overall rate and block length remain unchanged, the decoding complexity is at most doubled.  ...  A comparison to related methods for performance improvement of polar codes is drawn.  ...  Successive List Decoding As an improved version of the SC decoder for increased performance in the low-SNR regime, list decoding for polar codes has been proposed [3] .  ... 
arXiv:1312.2785v1 fatcat:yuu42tck6rc3pp32ifr4onqoz4

A Serially Concatenated Coding Scheme of Polar Code and the Improved Belief Propagation Decoding Algorithm

Xingcheng Liu, Yinyou Mao, Dong Yang
2020 IET Communications  
The novel belief propagation (BP) decoding algorithm addresses two issues that are present in the currently available BP decoding algorithms.  ...  The proposed BP decoding algorithm is based on right-directed message processing, which effectively improves the decoding performance.  ...  In addition, we plan to study the application in the BP list decoding algorithm, and explore the performance improvement of the concatenated code after paying a certain spatial complexity.  ... 
doi:10.1049/iet-com.2019.0887 fatcat:eeypuyfnejc3zl4aguveu7gaee

An Enhanced Decoding Algorithm for Coded Compressed Sensing with Applications to Unsourced Random Access

Vamsi K. Amalladinne, Jamison R. Ebert, Jean-Francois Chamberland, Krishna R. Narayanan
2022 Sensors  
In this article, an enhanced decoding algorithm is presented for a concatenated coding structure consisting of a wide range of inner codes and an outer tree-based code.  ...  This enhanced decoding algorithm is applied to two existing URA algorithms, and the performance benefits of the algorithm are characterized. Findings are supported by numerical simulations.  ...  The receiver architecture presented in [21] features a concatenated code, where the inner code C is decoded using a covariance-based activity detection (AD) algorithm and the outer tree code T is decoded  ... 
doi:10.3390/s22020676 pmid:35062636 pmcid:PMC8779509 fatcat:ctq5m6bcwnefddarudk5ige7ly

Page 9503 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
Summary: “A polynomial-time soft-decision decoding algorithm for Reed-Solomon codes is developed.  ...  Such nicely list decodable codes are then used as inner codes in a suitable concatenation scheme to give a uniformly constructive family of asymptotically good bi- nary linear codes of rate Q(e?  ... 

Reliability Level List Based Iterative SISO Decoding Algorithm for Block Turbo Codes

V Sudharsan, V Vijay Karthik, B Yamuna
2018 TELKOMNIKA (Telecommunication Computing Electronics and Control)  
An iterative Reliability Level List (RLL) based soft-input soft-output (SISO) decoding algorithm has been proposed for Block Turbo Codes (BTCs).  ...  The algorithm ingeniously adapts the RLL based decoding algorithm for the constituent block codes, which is a soft-input hard-output algorithm.  ...  Tanner proposed a hard in hard out (HIHO) iterative decoding method for concatenated product block codes and these 'high code rate' concatenated codes found widespread applications in deep space communication  ... 
doi:10.12928/telkomnika.v16i5.7463 fatcat:mflvju3fo5azlcstpyjprcgp74

Graph-based iterative decoding algorithms for parity-concatenated trellis codes

Qi Wang, Lei Wei
2001 IEEE Transactions on Information Theory  
However, since the graph of the parity-concatenated code contains many short cycles, the conventional min-sum and sum-product algorithms cannot achieve near-optimal decoding.  ...  In this paper, we construct parity-concatenated trellis codes in which a trellis code is used as the inner code and a simple parity-check code is used as the outer code.  ...  ., for their constructive advice, which significantly improved the quality of this paper.  ... 
doi:10.1109/18.915663 fatcat:a6acmfdjwnecdfthxa2dghnhbi

Reed-Solomon decoding algorithms for digital audio broadcasting in the AM band

J.N. Laneman, C.-E.W. Sundberg
2001 IEEE transactions on broadcasting  
important for generating block detected-error flags for use in the error concealment, or error mitigation, algorithm in the audio decoder.  ...  We provide simulation results for a variety of decoding algorithms, including hard-decision decoding (HDD), successive-erasure decoding (SED), and fixed-erasure decoding (FED), and discuss the channel  ...  a soft-output Viterbi algorithm (SOVA) for TCM, adding to the decoder complexity in a concatenation approach.  ... 
doi:10.1109/11.948264 fatcat:i36xb6mi3jbefih6ism7zkeply
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