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Two observations concerning optimum cyclic burst-correcting codes

P. Heijnen, H. van Tilborg
1998 Discrete Mathematics  
., 1986) it is shown that for each integer b~> 1 infinitely many optimum cyclic b-burst correcting codes exist.  ...  In the first part of this correspondence the parameters of all optimum cyclic four-and five-burst-correcting codes are given explicitly. Tables are included.  ...  Decoding optimum burst-correcting codes Let C be an optimum b-burst-correcting code of length n = 2 m-1 generated by e(x)p(x).  ... 
doi:10.1016/s0012-365x(97)00083-6 fatcat:glpzqkma4zgxdbqgvqthsc5bfy

Page 8143 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
(NL-EIND; Eindhoven) Two observations concerning optimum cyclic burst-correcting codes. (English summary) Discrete Math. 184 (1998), no. 1-3, 111-120. Summary: “In [K. A. S.  ...  Theory 32 (1986), no. 6, 768-775; MR 88f:94049], it is shown that for each integer b > 1 infinitely many optimum cyclic 5-burst correcting codes exist.  ... 

Coding theory

W. Peterson, J. Massey
1963 IEEE Transactions on Information Theory  
Furthermore, very simple and efficient encoding and error-correcting equipment can be built for any burst-error-correcting cyclic code [791-WI, WI.  ...  These latter papers are to a large measure responsible for interest in cyclic codes for random-error and burst-error correction respectively.  ...  A large class of burst-error-correcting cyclic codes with small redundancy has been found by Fire Progress in the study of cyclic codes for random-error correction has been spurred by the interest and  ... 
doi:10.1109/tit.1963.1057847 fatcat:x57gshj7gzfcxaofzejrrmboze

Exponential Bounds on the Probability of Error for a Discrete Memoryless Channel

Samuel Kotz
1961 The Annals of Mathematical Statistics  
Furthermore, very simple and efficient encoding and error-correcting equipment can be built for any burst-error-correcting cyclic code [791-WI, WI.  ...  These latter papers are to a large measure responsible for interest in cyclic codes for random-error and burst-error correction respectively.  ...  A large class of burst-error-correcting cyclic codes with small redundancy has been found by Fire Progress in the study of cyclic codes for random-error correction has been spurred by the interest and  ... 
doi:10.1214/aoms/1177705062 fatcat:sty2imjgxjbx3l7woay6ichjzy

Page 404 of SMPTE Motion Imaging Journal Vol. 89, Issue 5 [page]

1980 SMPTE Motion Imaging Journal  
Fire codes correct most of the burst and random errors whereas the cyclic codes expand the correctable burst error length of fire codes and detect the remaining errors.  ...  A combination of fire codes and cyclic redundance check codes are adopted for error correction and detection.  ... 

Page 716 of Mathematical Reviews Vol. 51, Issue 2 [page]

1976 Mathematical Reviews  
The authors present three simple constructions of rate-1/n burst- correcting convolutional codes. The first two constructions pro- duce type B, codes that have an optimal guard-space-to-burst ratio.  ...  Some of these can correct as long a burst as theoretically possible. The third construction produces codes that correct low-density type-B, bursts of length rn.  ... 

Coding for error control

D. T. Tang, R. T. Chien
1969 IBM Systems Journal  
I'rom the preceding, we observe that a ¢-error-correcting code is capable of detecting all combinations of 2¢ errors, and a burst-b- correcting code is capable of detecting any two bursts of length b or  ...  Kasami, “Optimum shortened cyclic codes for burst-error-correction,”’ IEEE Transactions on Information Theory IT-9, No. 2, 105-109 (April 1963). . L. D.  ... 
doi:10.1147/sj.81.0048 fatcat:yyoy4ysvzrhxppmr6fq673hkuu

Fire codes capable of correcting bursts beyond their guaranteed burst-correcting capabilities

Wei Zhou, Shu Lin, Khaled Abdel-Ghaffar
2016 2016 Information Theory and Applications Workshop (ITA)  
Fire codes are the most well-known class of burstcorrecting codes. They are designed to correct bursts up to a given guaranteed burst-correcting capability.  ...  It is shown that each class contains an infinite number of Fire codes that attain the maximum burst-correcting capability.  ...  Note that all these codes have the same length 1023, the same redundancy 13, and the same guaranteed burst correcting capability two.  ... 
doi:10.1109/ita.2016.7888192 dblp:conf/ita/ZhouLA16 fatcat:lyoblnjaz5anlh73nlpubg6ff4

Adaptive Channel Coding and Modulation Scheme Selection for Achieving High Throughput in Wireless Networks

Atif Sharif, Vidyasagar M. Potdar, Rana Fayyaz Ahmad
2010 2010 IEEE 24th International Conference on Advanced Information Networking and Applications Workshops  
GCC are based on binary cyclic codes. The criterion of the proposed research is to optimize the throughput of a wireless system.  ...  An adaptive coding scheme is proposed by using Generalized Concatenated Codes (GCC), which have simple structure and are designed in such a way that they are best suited for fading channels.  ...  One important property of product codes is burst error correction. Product codes are serially concatenated codes [12] .  ... 
doi:10.1109/waina.2010.197 dblp:conf/aina/SharifPA10 fatcat:w7v3euafnvatrm7lzvyo7bkpje

On Construction of Moderate-Length LDPC Codes over Correlated Erasure Channels

G. Liva, B. Matuz, Z. Katona, E. Paolini, M. Chiani
2009 2009 IEEE International Conference on Communications  
In this paper, the maximum tolerable erasure burst length (MTBL) is adopted as a simple metric for measuring the code robustness to the channel correlation.  ...  The design of moderate-length erasure correcting low-density parity-check (LDPC) codes over correlated erasure channels is considered.  ...  If the pivot swapping makes the burst length L+1 correctable for all burst positions, then L max is set to L + 1 and the burst length L + 2 is considered.  ... 
doi:10.1109/icc.2009.5199238 dblp:conf/icc/LivaMKPC09 fatcat:6mg2bv6ijnaqxdppy2dwxzspaa

Continuous error detection (CED) for reliable communication

R. Anand, K. Ramchandran, I.V. Kozintsev
2001 IEEE Transactions on Communications  
inner error-correction code and an outer error-detection code; and 3) reduced state sequence estimation (RSSE) for channels with memory.  ...  Block Cyclic Redundancy Check (CRC) codes represent a popular and powerful class of error detection techniques used almost exclusively in modern data communication systems.  ...  The source data stream has taken symbols at a time and encoded using a cyclic code to symbols. Since the code is cyclic, it can detect all bursts of error of length or less.  ... 
doi:10.1109/26.950341 fatcat:g3vlpzbwrbhqla6qco3mxpy4fm

Reversible codes

James L. Massey
1964 Information and Control  
However, a decoder operating over the increased constraint ]ength of the augmented code could give better error-correction. Two points concerning the augmented code deserve emphasis.  ...  AUGMENTATION OF NONREVERSIBLE CONVOLUTIONAL CODES At present, only a few specific classes of convolutional codes are known, viz. the burst-correcting codes of Hagelbarger (1959) and a few classes of random-error-correction  ... 
doi:10.1016/s0019-9958(64)90438-3 fatcat:dtq3li2ug5eoxnnhs2le6lc4ce

Sensitivity of coded mask telescopes

Gerald K. Skinner
2008 Applied Optics  
Simple formulae are often used to estimate the sensitivity of coded mask X-ray or gamma-ray telescopes, but these are strictly only applicable if a number of basic assumptions are met.  ...  We derive more general expressions for the Poisson-noise-limited sensitivity of astronomical telescopes using the coded mask technique, noting explicitly in what circumstances they are applicable.  ...  Thus the results are most directly applicable in the case of short observations of relatively bright sources (e.g. gamma-ray bursts) or where the design or observation strategy is such as to minimize such  ... 
doi:10.1364/ao.47.002739 pmid:18493279 fatcat:drwglemzxves5njevmcm6tqwea

Channel Coding: The Road to Channel Capacity [article]

Daniel J. Costello Jr., G. David Forney Jr
2006 arXiv   pre-print
Starting from Shannon's celebrated 1948 channel coding theorem, we trace the evolution of channel coding from Hamming codes to capacity-approaching codes.  ...  We trace the antecedents of today's capacity-approaching codes: convolutional codes, concatenated codes, and other probabilistic coding schemes.  ...  The two-stage decoder shown in Figure 5 is not optimum, but is capable of correcting a wide variety of error patterns.  ... 
arXiv:cs/0611112v1 fatcat:iwrrtx7mpfhgzfenehztfi5vyy

Channel coding: The road to channel capacity

Daniel J. Costello, G. David Forney
2007 Proceedings of the IEEE  
| Starting from Shannon's celebrated 1948 channel coding theorem, we trace the evolution of channel coding from Hamming codes to capacity-approaching codes.  ...  We trace the antecedents of today's capacity-approaching codes: convolutional codes, concatenated codes, and other probabilistic coding schemes.  ...  The two-stage decoder shown in Fig. 5 is not optimum, but is capable of correcting a wide variety of error patterns.  ... 
doi:10.1109/jproc.2007.895188 fatcat:pftdplkbergcbpkra6ddfwjtpa
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