Interleaved constrained codes with markers correcting bursts of insertions or deletions
- Smith, Dylan, Swart, Theo G., Abdel-Ghaffar, Khaled A. S., Ferreira, Hendrik C., Cheng, Ling
- Authors: Smith, Dylan , Swart, Theo G. , Abdel-Ghaffar, Khaled A. S. , Ferreira, Hendrik C. , Cheng, Ling
- Date: 2017
- Subjects: Insertions and deletions , Burst error correction , Constrained codes
- Language: English
- Type: Article
- Identifier: http://ujcontent.uj.ac.za8080/10210/371036 , http://hdl.handle.net/10210/225979 , uj:22837 , Citation: Smith, D. 2017. Interleaved constrained codes with markers correcting bursts of insertions or deletions.
- Description: Abstract: We present the construction of interleaving arrays for correcting clusters as well as diffuse bursts of insertion or deletion errors in constrained data. In this construction, a constrained information sequence is systematically encoded by computing a small number of parity checks and inserting markers such that the resulting code word is also constrained. Insertions and deletions lead to a shift between successive markers which can thus be detected and recovered using the parity checks. In this paper, as an example, the scheme is developed for Manchester-encoded information sequences.
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- Authors: Smith, Dylan , Swart, Theo G. , Abdel-Ghaffar, Khaled A. S. , Ferreira, Hendrik C. , Cheng, Ling
- Date: 2017
- Subjects: Insertions and deletions , Burst error correction , Constrained codes
- Language: English
- Type: Article
- Identifier: http://ujcontent.uj.ac.za8080/10210/371036 , http://hdl.handle.net/10210/225979 , uj:22837 , Citation: Smith, D. 2017. Interleaved constrained codes with markers correcting bursts of insertions or deletions.
- Description: Abstract: We present the construction of interleaving arrays for correcting clusters as well as diffuse bursts of insertion or deletion errors in constrained data. In this construction, a constrained information sequence is systematically encoded by computing a small number of parity checks and inserting markers such that the resulting code word is also constrained. Insertions and deletions lead to a shift between successive markers which can thus be detected and recovered using the parity checks. In this paper, as an example, the scheme is developed for Manchester-encoded information sequences.
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Codes for correcting three or more adjacent deletions or insertions
- Cheng, Ling, Swart, Theo G., Ferreira, Hendrik C., Abdel-Ghaffar, Khaled A. S.
- Authors: Cheng, Ling , Swart, Theo G. , Ferreira, Hendrik C. , Abdel-Ghaffar, Khaled A. S.
- Date: 2014
- Subjects: Correction codes
- Type: Article
- Identifier: uj:4750 , ISSN 978-1-4244-7891-0 , http://hdl.handle.net/10210/11736
- Description: Codes are presented that can correct the deletion or the insertion of a predetermined number of adjacent bits greater than or equal to three. This extends the constructions of codes beyond those proposed by Levenshtein fifty years ago to correct one or two adjacent deletions or insertions.
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- Authors: Cheng, Ling , Swart, Theo G. , Ferreira, Hendrik C. , Abdel-Ghaffar, Khaled A. S.
- Date: 2014
- Subjects: Correction codes
- Type: Article
- Identifier: uj:4750 , ISSN 978-1-4244-7891-0 , http://hdl.handle.net/10210/11736
- Description: Codes are presented that can correct the deletion or the insertion of a predetermined number of adjacent bits greater than or equal to three. This extends the constructions of codes beyond those proposed by Levenshtein fifty years ago to correct one or two adjacent deletions or insertions.
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Moment balancing templates: constructions to add insertion/deletion correction capability to error correcting or constrained codes
- Ferreira, Hendrik C., Abdel-Ghaffar, Khaled A. S., Cheng, Ling, Swart, Theo G., Ouahada, Khmaies
- Authors: Ferreira, Hendrik C. , Abdel-Ghaffar, Khaled A. S. , Cheng, Ling , Swart, Theo G. , Ouahada, Khmaies
- Date: 2009
- Subjects: Constrained code , Extended codes , Insertions/deletions , Moment function , Number theoretic codes
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/20120 , uj:16069 , ISSN: 0018-9448 , Citation: Ferreira, H.C. et al. 2009. Moment balancing templates: constructions to add insertion/deletion correction capability to error correcting or constrained codes. IEEE Transactions on Information Theory, 55(8):3494–3500.
- Description: Abstract: Templates are constructed to extend arbitrary additive error correcting or constrained codes, i.e., additional redundant bits are added in selected positions to balance the moment of the codeword. The original codes may have error correcting capabilities or constrained output symbols as predetermined by the usual communication system considerations, which are retained after extending the code. Using some number theoretic constructions in the literature, insertion/deletion correction can then be achieved. If the template is carefully designed, the number of additional redundant bits for the insertion/deletion correction can be kept small—in some cases of the same order as the number of parity bits in a Hamming code of comparable length.
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- Authors: Ferreira, Hendrik C. , Abdel-Ghaffar, Khaled A. S. , Cheng, Ling , Swart, Theo G. , Ouahada, Khmaies
- Date: 2009
- Subjects: Constrained code , Extended codes , Insertions/deletions , Moment function , Number theoretic codes
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/20120 , uj:16069 , ISSN: 0018-9448 , Citation: Ferreira, H.C. et al. 2009. Moment balancing templates: constructions to add insertion/deletion correction capability to error correcting or constrained codes. IEEE Transactions on Information Theory, 55(8):3494–3500.
- Description: Abstract: Templates are constructed to extend arbitrary additive error correcting or constrained codes, i.e., additional redundant bits are added in selected positions to balance the moment of the codeword. The original codes may have error correcting capabilities or constrained output symbols as predetermined by the usual communication system considerations, which are retained after extending the code. Using some number theoretic constructions in the literature, insertion/deletion correction can then be achieved. If the template is carefully designed, the number of additional redundant bits for the insertion/deletion correction can be kept small—in some cases of the same order as the number of parity bits in a Hamming code of comparable length.
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Moment balancing templates: Universal constructions to add insertion/deletion correction capability to arbitrary error correcting or constrained codes
- Ferreira, Hendrik C., Abdel-Ghaffar, Khaled A. S., Cheng, Ling, Swart, Theo G.
- Authors: Ferreira, Hendrik C. , Abdel-Ghaffar, Khaled A. S. , Cheng, Ling , Swart, Theo G.
- Date: 2007
- Subjects: Balancing templates , Arbitrary error correcting , Constrained codes
- Language: English
- Type: Conference Proceedings
- Identifier: http://hdl.handle.net/10210/18397 , uj:15993 , Citation: Ferreira, H.C. et al. 2007. Moment balancing templates: Universal constructions to add insertion/deletion correction capability to arbitrary error correcting or constrained codes. Proceedings of the IEEE International Symposium on Information Theory, 24-29 June, 2007, Nice, France.
- Description: Abstract: We investigate extending a chosen block or convolutional code which has additive error correction capability, as predetermined by the usual communication systems or coding considerations. Our extension involves constructing a template to add additional redundant bits in positions, selected to balance the moment of the code word. Using some number theoretic constructions in the literature, insertion/deletion correction can then be achieved. If the template is carefully designed, the number of additional redundant bits for the insertion/deletion correction can be kept small - in some cases of the same order as for Hamming codes. Our construction technique can also be used for the systematic encoding of number theoretic codes, and furthermore have implications for other coding techniques utilizing the moment function, such as codes correcting asymmetrical errors, spectral shaping codes, or constant weight codes.
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- Authors: Ferreira, Hendrik C. , Abdel-Ghaffar, Khaled A. S. , Cheng, Ling , Swart, Theo G.
- Date: 2007
- Subjects: Balancing templates , Arbitrary error correcting , Constrained codes
- Language: English
- Type: Conference Proceedings
- Identifier: http://hdl.handle.net/10210/18397 , uj:15993 , Citation: Ferreira, H.C. et al. 2007. Moment balancing templates: Universal constructions to add insertion/deletion correction capability to arbitrary error correcting or constrained codes. Proceedings of the IEEE International Symposium on Information Theory, 24-29 June, 2007, Nice, France.
- Description: Abstract: We investigate extending a chosen block or convolutional code which has additive error correction capability, as predetermined by the usual communication systems or coding considerations. Our extension involves constructing a template to add additional redundant bits in positions, selected to balance the moment of the code word. Using some number theoretic constructions in the literature, insertion/deletion correction can then be achieved. If the template is carefully designed, the number of additional redundant bits for the insertion/deletion correction can be kept small - in some cases of the same order as for Hamming codes. Our construction technique can also be used for the systematic encoding of number theoretic codes, and furthermore have implications for other coding techniques utilizing the moment function, such as codes correcting asymmetrical errors, spectral shaping codes, or constant weight codes.
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