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Tolhuizen, “On q-ary codes correcting all unidirectional errors of a limited magnitude

by R. Ahlswede, H. Aydinian, L. H. Khachatrian, L. M. G. M Tolhuizen - in Proceedings of the International Workshop on Algebraic and Combinatorial Coding Theory (ACCT , 2004
"... Dedicated to the memory of Rom Varshamov We consider codes over the alphabet Q = {0,1,...,q − 1} intended for the control of unidirectional errors of level ℓ. That is, the transmission channel is such that the received word cannot contain both a component larger than the transmitted one and a compon ..."
Abstract - Cited by 11 (2 self) - Add to MetaCart
component smaller than the transmitted one. Moreover, the absolute value of the difference between a transmitted component and its received version is at most ℓ. We introduce and study q-ary codes capable of correcting all unidirectional errors of level ℓ. Lower and upper bounds for the maximal size

Loopy belief propagation for approximate inference: An empirical study. In:

by Kevin P Murphy , Yair Weiss , Michael I Jordan - Proceedings of Uncertainty in AI, , 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" -the use of Pearl's polytree algorithm in a Bayesian network with loops -can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon-limit performanc ..."
Abstract - Cited by 676 (15 self) - Add to MetaCart
Abstract Recently, researchers have demonstrated that "loopy belief propagation" -the use of Pearl's polytree algorithm in a Bayesian network with loops -can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon-limit

DRAFT Self-orthogonality of q-ary Images of q m-ary Codes

by Sundeep Balaji, Andrew Thangaraj , 2008
"... A code over GF(q m) can be imaged or expanded into a code over GF(q) using a basis for the extension field over the base field. The properties of such an image depend on the original code and the basis chosen for imaging. Problems relating the properties of a code and its image with respect to a bas ..."
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-orthogonal for all bases if and only if trace of the code is self-orthogonal, except for the case of binary images of 4-ary codes. The conditions are particularly simple to state and apply for cyclic codes. To illustrate a possible application, new quantum error-correcting codes have been constructed with larger

DRAFT Self-orthogonality of q-ary Images of q m-ary Codes

by Sundeep B, Andrew Thangaraj , 2008
"... A code over GF(q m) can be imaged or expanded into a code over GF(q) using a basis for the extension field over the base field. The properties of such an image depend on the original code and the basis chosen for imaging. Problems relating the properties of a code and its image with respect to a bas ..."
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-orthogonal for all bases if and only if trace of the code is self-orthogonal, except for the case of binary images of 4-ary codes. The conditions are particularly simple to state and apply for cyclic codes. To illustrate a possible application, new quantum error-correcting codes have been constructed with larger

Codes for Multi-Level Flash Memories: Correcting Asymmetric Limited-Magnitude Errors

by Yuval Cassuto, Moshe Schwartz, Vasken Bohossian, Jehoshua Bruck
"... Abstract — Several physical effects that limit the reliability and performance of Multilevel Flash memories induce errors that have low magnitude and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions f ..."
Abstract - Cited by 19 (6 self) - Add to MetaCart
Abstract — Several physical effects that limit the reliability and performance of Multilevel Flash memories induce errors that have low magnitude and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions

Unidirectional Error Control Codes and Related Combinatorial Problems

by R. Ahlswede, H. Aydinian, L. H. Khachatrian
"... q–ary codes capable of correcting all unidirectional errors of certain level 1 ≤ ℓ ≤ q − 2 are considered. We also discuss some related extremal combinatorial problems. 1 ..."
Abstract - Cited by 8 (0 self) - Add to MetaCart
q–ary codes capable of correcting all unidirectional errors of certain level 1 ≤ ℓ ≤ q − 2 are considered. We also discuss some related extremal combinatorial problems. 1

Limited magnitude error detecting codes over Zq

by Noha Elarief, Bella Bose
"... Abstract—The error detecting problem for limited magnitude errors over high radix channels is studied. In this error model, the error magnitude does not exceed a certain limit known beforehand. For asymmetric and unidirectional channels, both all and t error detecting codes are studied. Further, clo ..."
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Abstract—The error detecting problem for limited magnitude errors over high radix channels is studied. In this error model, the error magnitude does not exceed a certain limit known beforehand. For asymmetric and unidirectional channels, both all and t error detecting codes are studied. Further

Correcting limited-magnitude errors in the rank-modulation scheme

by Itzhak Tamo, Moshe Schwartz , 2010
"... Abstract—We study error-correcting codes for permutations under the infinity norm, motivated by a novel storage scheme for flash memories called rank modulation. In this scheme, a set of n flash cells are combined to create a single virtual multilevel cell. Information is stored in the permutation i ..."
Abstract - Cited by 37 (15 self) - Add to MetaCart
induced by the cell charge levels. Spike errors, which are characterized by a limited-magnitude change in cell charge levels, correspond to a low-distance change under the infinity norm. We define codes protecting against spike errors, called limitedmagnitude rank-modulation codes (LMRM codes

Conditional Random Network Coding in the Case of Transmission over q-ary Gilbert Elliot Channel

by Aicha Guefrachi, Sonia Zaibi, Ammar Bouallègue , 2013
"... The benefit of random linear network coding (RLNC) has been studied in wired and wireless networks. Furthermore, it has been shown that RLNC improves throughput, bandwidth and robustness to network changes or link failures, however it is highly susceptible to error propagation. As existing error c ..."
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correcting codes are not adapted to such errors, recently Kötter and Kschischang introduced a new subspace code in the context of a noncoherent transmission model. In this paper, we evaluate the performance of such code in the case of transmission over a network where each link is a q-ary Gilbert Elliot

Codes for Asymmetric Limited-Magnitude Errors with Application to Multi-Level Flash Memories

by Yuval Cassuto, Moshe Schwartz, Vasken Bohossian, Jehoshua Bruck
"... Several physical effects that limit the reliability and performance of Multilevel Flash Memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds ..."
Abstract - Cited by 30 (14 self) - Add to MetaCart
Several physical effects that limit the reliability and performance of Multilevel Flash Memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions
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