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Two-dimensional cyclic codes correcting known error patterns

Sung Whan Yoon, Jaekyun Moon
2012 2012 IEEE Global Communications Conference (GLOBECOM)  
1 This paper considers error-correcting codes designed to correct a finite set of known two-dimensional (2D) error patterns that can occur in a 2D array of bits.  ...  The specific codes designed in this paper are cyclic codes that can correct any single occurrences of dominant known error patterns that can occur anywhere in the 2D array.  ...  CONSTRUCTION OF ERROR-PATTERN-CORRECTING 2D CYCLIC CODES A.  ... 
doi:10.1109/glocom.2012.6503612 dblp:conf/globecom/YoonM12 fatcat:dm5z65leurbapcfnldqcwng36q

Two-Dimensional Cluster-Correcting Codes

M. Schwartz, T. Etzion
2005 IEEE Transactions on Information Theory  
We consider two-dimensional error-correcting codes capable of correcting a single arbitrary cluster of errors of size .  ...  We also construct 3-cluster-correcting codes and -straight-cluster-correcting codes. We conclude by improving the Reiger bound for two-dimensional cluster-correcting codes.  ...  Roth for providing Construction G and for many helpful discussions and Eitan Yaakobi for pointing out errors in an earlier version of the paper.  ... 
doi:10.1109/tit.2005.847726 fatcat:dch6u6hsbjcmnddfzvkp7wauvu

Transform Techniques for Error Control Codes

R. E. Blahut
1979 IBM Journal of Research and Development  
In particular, an errors-and-erasures decoderjor a BCH code is exhibited which has virtuully no additional computations over an errors-only decoder.  ...  By using the theory ofjinite5eld Fourier transforms, the subject o f error control codes is described in N language familiar to thejield of signal processing.  ...  A cyclic code with parity frequencies that are not contiguous. 3. A decoder for some of the (t + I)-error patterns in a terror-correcting Reed-Solomon code.  ... 
doi:10.1147/rd.233.0299 fatcat:txfqsqdsezak7ldzi73ckotuze

High Dimensional Error-Correcting Codes [article]

Eitan Yaakobi, Tuvi Etzion
2010 arXiv   pre-print
The codes can correct high dimensional errors which have the form of either small clusters, or confined to an area with a small radius. We also consider small number of errors in a small area.  ...  Also considered are clusters with small number of errors such as 2-bursts, two errors in various clusters, and three errors on a line.  ...  Given a set S with patterns of errors, the most natural and simple way to correct an error from S is to correct a box-error which contains all possible errors from S.  ... 
arXiv:0910.5697v2 fatcat:6nng5r7uerdxhaaslz5uaxdl3a

Multiple-burst-error correction by threshold decoding

L.R. Bahl, R.T. Chien
1969 Information and Control  
A class of cyclic product codes capable of correcting mtfltiple-burst errors is studied.  ...  A code of dimension p is constructed by forming the cyclic product of p one-dimensional single-parity-check codes of relatively prime block lengths.  ...  (Burton and Weldon, [3] ) It is known that the minimum distance of the code C ~ is 2 ~ and that the codewords of weight exactly 2 ~ are those patterns having nonzero digits at the corners of a p-dimensional  ... 
doi:10.1016/s0019-9958(69)90489-6 fatcat:74z4edt7bfebjbv7adgogjc7di

Error-Correction of Multidimensional Bursts [article]

Tuvi Etzion, Eitan Yaakobi
2007 arXiv   pre-print
Our main results are summarized as follows: 1) A construction of two-dimensional codes capable to correct a rectangular-error with considerably more flexible parameters from previously known constructions  ...  We use the previous constructions to correct a D-dimensional error whose shape is a D-dimensional Lee sphere. 4) Applying the coloring method to correct more efficiently a two-dimensional error whose shape  ...  This bound, known as the Reiger bound [14] , is attained for binary two-dimensional codes, which correct a rectangular error, constructed recently by Boyarinov [7] .  ... 
arXiv:0712.4096v1 fatcat:der2pwarfna7rgpqmps6y2cumq

Two-dimensional burst identification codes and their use in burst correction

K.A.S. Abdel-Ghaffar, R.J. McEliece, H.C.A. Van Tilborg
1988 IEEE Transactions on Information Theory  
Ahstrad-A new class of codes, called burst identification codes, is defined and studied. These codes can be used to determine the patterns of burst errors.  ...  Two-dimensional burst correcting codes can be easily constructed from burst identification codes. me resulting class of codes is simple to implement and has lower redundancy than other comparable codes  ...  and Imai [ l l ] has given a two-dimensional version of the error trapping algorithm which is well-known for decoding one-dimensional cyclic burst correcting codes [ 121.  ... 
doi:10.1109/18.6029 fatcat:cvzchik42jdltclcg4cl24vioq

Two-Dimensional Error-Pattern-Correcting Codes

Sung Whan Yoon, Jaekyun Moon
2015 IEEE Transactions on Communications  
Two-dimensional (2D) cyclic codes are presented which correct any single occurrence of known 2D error patterns within a 2D array of bits.  ...  A method to refine the syndrome sets is then presented for making each syndrome set to contain distinct members, thereby guaranteeing full correction capability for the given list of known error patterns  ...  General Description of Two-Dimensional Cyclic Codes The following description of general 2D cyclic codes is based on Imai's work [10] , [11] .  ... 
doi:10.1109/tcomm.2015.2438869 fatcat:c7h3gsxavzbmjjmr5ms6d3vffu

Page 816 of Mathematical Reviews Vol. 47, Issue 3 [page]

1974 Mathematical Reviews  
set of error patterns to be corrected.” 4708 Koshy, Thomas Quasi-cyclic product codes.  ...  A new product of quasi-cyclic codes of the same rate is defined and it is proved that the product of two quasi-cyclic codes of the same rate is also a quasi-cyclic code of the same rate.  ... 

Finite Geometry Permutation Decoding for Wireless Sensor Network Applications

2017 Sensors and materials  
The two-dimensional construction for square wireless sensor networks (WSNs) is suitable for employing channel coding, especially product codes and finite geometry codes, and for detecting multiple error  ...  To improve the drawback of the less correcting capacity, the GPD algorithm not only gives better bit error rates at low decoding complexity but also provides a new solution suitable for decoding in two-dimensional  ...  error-correcting codes.  ... 
doi:10.18494/sam.2017.1477 fatcat:7kc5xmcrvjh6zk5sh6jvqsyvr4

Cyclic Low Density Parity Check Codes With The Optimum Burst Error Correcting Capability

Sina Vafi
2020 IEEE Access  
There are several methods for constructing single or multiple dimensional cyclic codes suitable for the correction of burst errors [2] [3] .  ...  As expected, multi-dimensional codes provide better error protection than the one-dimensional codes as they can correct a number of single burst errors but at the expense of more complexity in design due  ... 
doi:10.1109/access.2020.3032837 fatcat:u24cj6on3faprkrmbdw4mkwshi

Cumulative subject index volumes 33–35

1977 Information and Control  
W Weight Lee, burst correcting codes, 33, 210 of code words, cyclic codes, 34, 130 Weight-balanced tree bound for, improved, 34, 148 rate distortion Z z~ codes over, for any positive m, 35  ...  : definition, structure, and examples, 33, 56 two-dimensional cyclic, theory, 34, 1 over Z~, for any positive m, 35, 48 Coding channel and source, probability lower bound method, 33, 367 sliding  ... 
doi:10.1016/s0019-9958(77)90187-5 fatcat:jaxd23nbmva5hdnq37lof736um

Page 7042 of Mathematical Reviews Vol. , Issue 91M [page]

1991 Mathematical Reviews  
The author investigates the Varshamov codes, which are known to correct r errors of types 0 — 1.  ...  These codes are nonsys- tematic f-error-correcting and all-unidirectional-error-detecting (t- EC/AUED) codes.  ... 

RUNE-Tag: A high accuracy fiducial marker with strong occlusion resilience

Filippo Bergamasco, Andrea Albarelli, Emanuele Rodola, Andrea Torsello
2011 CVPR 2011  
Further, applying a dot pattern scheme derived from errorcorrecting codes, allows for robustness with respect to very large occlusions.  ...  In addition, the design of the marker itself is flexible enough to accommodate different requirements in terms of pose accuracy and number of patterns.  ...  In this paper we are restricting our analysis to the correction of random errors or erasures, but it is worth noting that cyclic codes have been used to detect and correct burst errors, i.e. errors that  ... 
doi:10.1109/cvpr.2011.5995544 dblp:conf/cvpr/BergamascoART11 fatcat:57ubgnfm4zgodg3ke5wg24kqlq

Page 2852 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
In the present paper it is shown that each such sequence is balanced and, moreover, that the dual of the linear cyclic code generated by the sequence and its cyclic shifts, is a triple-error correcting  ...  Vijay (1-SCA; Los Angeles, CA) On a conjectured ideal autocorrelation sequence and a related triple-error correcting cyclic code. (English summary) IEEE Trans. Inform.  ... 
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