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Adaptive Single-Trial Error/Erasure Decoding of Reed-Solomon Codes [article]

Christian Senger, Vladimir R. Sidorenko, Steffen Schober, Martin Bossert, Victor V. Zyablov
2011 arXiv   pre-print
In this paper we investigate adaptive single-trial error/erasure decoding of Reed-Solomon codes, i.e. we derive an adaptive erasing strategy which minimizes the residual codeword error probability after  ...  Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities.  ...  INTRODUCTION Using algebraic error/erasure decoders for pseudo-soft decoding of Reed-Solomon (RS) codes dates back to Forney [1] , [2] .  ... 
arXiv:1104.0576v1 fatcat:3rc36d3murdwrh5koahyttbg3a

Asymptotic single-trial strategies for GMD decoding with arbitrary error-erasure tradeoff

J. H. Weber, V. R. Sidorenko, C. Senger, K. A. S. Abdel-Ghaffar
2012 Problems of Information Transmission  
We investigate singletrial strategies for GMD decoding with arbitrary error-erasure tradeoff, based on either erasing a fraction of the received symbols or erasing all symbols whose reliability values  ...  The fraction/threshold may be either static or adaptive, where adaptive means that the erasing is a function of the channel output.  ...  In the classical case one has λ = 2, while smaller values of λ are of interest for decoding certain classes of punctured Reed-Solomon codes as well as for some modern algebraic decoders like the Sudan  ... 
doi:10.1134/s0032946012040023 fatcat:l6eero7zv5eybadken5bnmtcg4

Guruswami--Sudan List Decoding for Complex Reed--Solomon Codes [article]

Mostafa H. Mohamed and Sven Puchinger and Martin Bossert
2016 arXiv   pre-print
We analyze the Guruswami--Sudan list decoding algorithm for Reed--Solomon codes over the complex field for sparse recovery in Compressed Sensing.  ...  This method also allows to obtain a unique solution of the recovery problem. The approach is numerically evaluated and shown to improve upon recently proposed decoding techniques.  ...  ACKNOWLEDGMENTS The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.  ... 
arXiv:1611.07811v1 fatcat:zqmnlrqzebafnobbnfdwhqwkfy

Reduced GMD decoding

J.H. Weber, K.A.S. Abdel-Ghaffar
2003 IEEE Transactions on Information Theory  
In GMD decoding, symbols received from the channel may be erased before being fed into an algebraic error-erasure decoder for error correction, in subsequent or simultaneous trials with different erasing  ...  A framework is presented for generalized minimum distance (GMD) decoding with a limited number of decoding trials and a restricted set of reliability values.  ...  ACKNOWLEDGMENT The authors wish to thank the anonymous reviewers and the Associate Editor for their suggestions that improved the quality of this correspondence.  ... 
doi:10.1109/tit.2003.809504 fatcat:zvtcvcyrxvag7nsrc66kdh55qe

Towards efficient proofs of retrievability

Jia Xu, Ee-Chien Chang
2012 Proceedings of the 7th ACM Symposium on Information, Computer and Communications Security - ASIACCS '12  
Proofs of Retrievability (POR) is a cryptographic formulation for remotely auditing the integrity of files stored in the cloud, without keeping a copy of the original files in local storage.  ...  Later, Alice can periodically and remotely verify the integrity of her data file using the authentication data, without retrieving back the data file.  ...  Apply a rate-ρ error erasure code (e.g.  ... 
doi:10.1145/2414456.2414503 dblp:conf/ccs/XuC12 fatcat:3xy7ehfcpfd4pdjjhhtnbqbirm

Rank-Metric Codes and Their Applications [article]

Hannes Bartz, Lukas Holzbaur, Hedongliang Liu, Sven Puchinger, Julian Renner, Antonia Wachter-Zeh
2022 arXiv   pre-print
In code-based cryptography, the hardness of the corresponding generic decoding problem can lead to systems with reduced public-key size.  ...  In distributed data storage, codes in the rank metric have been used repeatedly to construct codes with locality, and in coded caching, they have been employed for the placement of coded symbols.  ...  Acknowledgements The work of L. Holzbaur and A. Wachter  ... 
arXiv:2203.12384v1 fatcat:brysqya7ynem5i25adxfwf5vl4

Cooperating error-correcting codes and their decoding [article]

LMGM Ludo Tolhuizen, JH Van Lint, HCA Henk Van Tilborg
Janssen for finding the asymptotical behaviour of Sn described in Subsection 7.4.3. Acknowledgments The authors thank their colleagues H.D.L. Hollmann, A.G.C.  ...  Random error and burst correction by iterated codes. IEEE Trans. Inform. Th., IT-18(1):182-185, January 1972. [16] S. Wainberg. Error-erasure decoding of product codes. IEEE Trans. Inform.  ...  A new efficient error-erasure location scheme in gmd decoding. In Proc. 1993 IEEE Int. Symp. Inform. Theory, page 33, San Antonio, TX, January 1993. [9] U.K. Sorger.  ... 
doi:10.6100/ir462079 fatcat:uol5b54ibneaxir2dwj3fwcri4

Memory protection techniques for DRAM scaling-induced errors [article]

Seong-Lyong Gong
Reed-Solomon (RS) codes offer a straightforward way to achieve Chipkill protection.  ...  AMD published a Chipkill option for ×4 ECC DIMMs, using an 8b-symbol RS (18, 16 ) code [12] ; RS (18, 16) denotes a Reed-Solomon code with 18 symbols per codeword, of which 16 store data.  ... 
doi:10.15781/t2df6kn9f fatcat:heogzmuyzrhdvgng3ows2vr6de

Cryptography based on the Hardness of Decoding

Nico Marcel Döttling
This thesis provides progress in the fields of for lattice and coding based cryptography.  ...  The first contribution consists of constructions of IND-CCA2 secure public key cryptosystems from both the McEliece and the low noise learning parity with noise assumption.  ...  In case the code-alphabet is binary, we refer to symbol errors as bit errors. Erasure Errors Erasure errors model the detectable loss of information in a transmitted message.  ... 
doi:10.5445/ir/1000041110 fatcat:ntqa7i3wwzh5djmxsxuagdq4em

Digital watermarking and data hiding in multimedia

Abdulaziz, Nidhal Kadhim, 1958-
182 decoded for consumption according to usage rights associated with the content (quoted from a web paper by Leonardo Chiariglione, Convener, MPEG; (  ...  References 183 References ACKNOWLEDGMENTS The author would like to thank University of Southern California, Signal and Image processing Institute (USC-SIPI) Image Database for using their classic  ...  Error correcting codes provide coders with a tool to recover lost information such as errors, erasures and deletions.  ... 
doi:10.4225/03/59d44ace2f9d5 fatcat:6ah66x7prbbhvp4mu2yplgtzey

Signal and receiver design for high density digital magnetic tape recording

Roger William Wood
The playback receiver comprised a fixed pre-filter followed by an adaptive seven-tap transversal, filter.  ...  In particular, erasure detection and interleaved block coding proved to be useful techniques. The application of decision feedback was found to provide only marginal improvements in performance.  ...  The elements of the -137 -outer code may be rendered independent by interleaving although Reed-Solomon codes [165, 243] exhibit useful burst error/erasure correction capability.  ... 
doi:10.14288/1.0065619 fatcat:3ibsv22nrzfkzesggu6eacnxki