A note on non-binary multiple insertion/deletion correcting codes
- Paluncic, Filip, Swart, Theo G., Weber, Jos H., Ferreira, Hendrik C., Clarke, Willem A.
- Authors: Paluncic, Filip , Swart, Theo G. , Weber, Jos H. , Ferreira, Hendrik C. , Clarke, Willem A.
- Date: 2011
- Subjects: Insertion/deletion , Correcting codes
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/20202 , uj:16077 , ISBN: 978-1-4577-0437-6 , Citation: Paluncic, F. et al. 2011. A note on non-binary multiple insertion/deletion correcting codes. Proceedings of the IEEE Information Theory Workshop, 16-20 October, 2011, Paraty, Brazil.
- Description: Abstract: We propose the construction of a non-binary multiple insertion/deletion correcting code based on a binary multiple insertion/deletion correcting code. In essence, it is a generalisation of Tenengol’ts’ non-binary single insertion/deletion correcting code. We evaluate the cardinality of the proposed construction based on the asymptotic upper bound on the cardinality of a maximal binary multiple insertion/deletion correcting code derived by Levenshtein.
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- Authors: Paluncic, Filip , Swart, Theo G. , Weber, Jos H. , Ferreira, Hendrik C. , Clarke, Willem A.
- Date: 2011
- Subjects: Insertion/deletion , Correcting codes
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/20202 , uj:16077 , ISBN: 978-1-4577-0437-6 , Citation: Paluncic, F. et al. 2011. A note on non-binary multiple insertion/deletion correcting codes. Proceedings of the IEEE Information Theory Workshop, 16-20 October, 2011, Paraty, Brazil.
- Description: Abstract: We propose the construction of a non-binary multiple insertion/deletion correcting code based on a binary multiple insertion/deletion correcting code. In essence, it is a generalisation of Tenengol’ts’ non-binary single insertion/deletion correcting code. We evaluate the cardinality of the proposed construction based on the asymptotic upper bound on the cardinality of a maximal binary multiple insertion/deletion correcting code derived by Levenshtein.
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Balanced runlength limited codes using Knuth’s algorithm
- Immink, Kees A. Schouhamer, Weber, Jos H., Ferreira, Hendrik C.
- Authors: Immink, Kees A. Schouhamer , Weber, Jos H. , Ferreira, Hendrik C.
- Date: 2011
- Subjects: Balanced codes , Bipolar codewords , Knuth’s algorithm
- Type: Article
- Identifier: uj:6263 , ISSN 6033677 , http://hdl.handle.net/10210/8252
- Description: Knuth published a very simple algorithm for constructing bipolar codewords with equal numbers of +1’s and -1’s, called balanced codes. In our paper we will present new code constructions that generate balanced runlength limited sequences using a modification of Knuth’s algorithm.
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- Authors: Immink, Kees A. Schouhamer , Weber, Jos H. , Ferreira, Hendrik C.
- Date: 2011
- Subjects: Balanced codes , Bipolar codewords , Knuth’s algorithm
- Type: Article
- Identifier: uj:6263 , ISSN 6033677 , http://hdl.handle.net/10210/8252
- Description: Knuth published a very simple algorithm for constructing bipolar codewords with equal numbers of +1’s and -1’s, called balanced codes. In our paper we will present new code constructions that generate balanced runlength limited sequences using a modification of Knuth’s algorithm.
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Concatenated permutation block codes based on set partitioning for substitution and deletion error-control
- Heymann, Reolyn, Weber, Jos H., Swart, Theo G., Ferreira, Hendrik C.
- Authors: Heymann, Reolyn , Weber, Jos H. , Swart, Theo G. , Ferreira, Hendrik C.
- Date: 2013
- Subjects: Binary data , Permutation codes
- Type: Article
- Identifier: uj:4853 , http://hdl.handle.net/10210/12520
- Description: A new class of permutation codes is presented where, instead of considering one permutation as a codeword, codewords consist of a sequence of permutations. The advantage of using permutations, i.e. their favourable symbol diversity properties, is preserved. Additionally, using sequences of permutations as codewords, code rates close to the optimum rate can be achieved. Firstly, the complete set of permutations is divided into subsets by using set partitioning. Binary data is then mapped to permutations from these subsets. These permutations, together with a parity permutation, will form the codeword. Two constructions will be presented: one capable of detecting and correcting substitution errors and the other capable of detecting and correcting either substitution or deletion errors.
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- Authors: Heymann, Reolyn , Weber, Jos H. , Swart, Theo G. , Ferreira, Hendrik C.
- Date: 2013
- Subjects: Binary data , Permutation codes
- Type: Article
- Identifier: uj:4853 , http://hdl.handle.net/10210/12520
- Description: A new class of permutation codes is presented where, instead of considering one permutation as a codeword, codewords consist of a sequence of permutations. The advantage of using permutations, i.e. their favourable symbol diversity properties, is preserved. Additionally, using sequences of permutations as codewords, code rates close to the optimum rate can be achieved. Firstly, the complete set of permutations is divided into subsets by using set partitioning. Binary data is then mapped to permutations from these subsets. These permutations, together with a parity permutation, will form the codeword. Two constructions will be presented: one capable of detecting and correcting substitution errors and the other capable of detecting and correcting either substitution or deletion errors.
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Efficient balancing of q-ary sequences with parallel decoding
- Swart, Theo G., Weber, Jos H.
- Authors: Swart, Theo G. , Weber, Jos H.
- Date: 2009
- Subjects: Q-ary sequences , Parallel decoding
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/18468 , uj:16003 , Citation: Swart, T.G. & Weber, J.H. 2009. Efficient balancing of q-ary sequences with parallel decoding. Proceedings of the IEEE International Symposium on Information Theory, 28 June-3 July, South Korea.
- Description: Abstract: Balancing of q-ary sequences, using a generalization of Knuth’s efficient parallel balancing scheme, is considered. It is shown that the new general scheme is as simple as the original binary scheme, which lends itself to parallel decoding of the balanced sequences.
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- Authors: Swart, Theo G. , Weber, Jos H.
- Date: 2009
- Subjects: Q-ary sequences , Parallel decoding
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/18468 , uj:16003 , Citation: Swart, T.G. & Weber, J.H. 2009. Efficient balancing of q-ary sequences with parallel decoding. Proceedings of the IEEE International Symposium on Information Theory, 28 June-3 July, South Korea.
- Description: Abstract: Balancing of q-ary sequences, using a generalization of Knuth’s efficient parallel balancing scheme, is considered. It is shown that the new general scheme is as simple as the original binary scheme, which lends itself to parallel decoding of the balanced sequences.
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Extension of Knuth's balancing algorithm with error correction
- Weber, Jos H., Ferreira, Hendrik C., Immink, Kees A. Schouhamer
- Authors: Weber, Jos H. , Ferreira, Hendrik C. , Immink, Kees A. Schouhamer
- Date: 2011
- Subjects: Error correction , Knuth's balancing algorithm
- Type: Article
- Identifier: uj:6083 , ISSN 9789081721905 , http://hdl.handle.net/10210/10931
- Description: Knuth's celebrated balancing method consists of inverting the first z bits in a binary information sequence, such that the resulting sequence has as many ones as zeroes, and communicating the index z to the receiver through a short balanced prefix. In the proposed method, Knuth's scheme is extended with error-correcting capabilities, where it is allowed to give unequal protection levels to the prefix and the payload. An analysis with respect to the redundancy of the proposed method is performed, showing good results while maintaining the simplicity features of the original scheme.
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- Authors: Weber, Jos H. , Ferreira, Hendrik C. , Immink, Kees A. Schouhamer
- Date: 2011
- Subjects: Error correction , Knuth's balancing algorithm
- Type: Article
- Identifier: uj:6083 , ISSN 9789081721905 , http://hdl.handle.net/10210/10931
- Description: Knuth's celebrated balancing method consists of inverting the first z bits in a binary information sequence, such that the resulting sequence has as many ones as zeroes, and communicating the index z to the receiver through a short balanced prefix. In the proposed method, Knuth's scheme is extended with error-correcting capabilities, where it is allowed to give unequal protection levels to the prefix and the payload. An analysis with respect to the redundancy of the proposed method is performed, showing good results while maintaining the simplicity features of the original scheme.
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Prefixless q-ary balanced codes with fast syndrome-based error correction
- Swart, Theo G., Weber, Jos H., Schouhamer Immink, Kees A.
- Authors: Swart, Theo G. , Weber, Jos H. , Schouhamer Immink, Kees A.
- Date: 2018
- Subjects: Balanced code , Constrained code , error correction
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/279793 , uj:30054 , Citation: Swart, T.G., Weber, J.H. & Schouhamer Immink, K.A. 2018. Prefixless q-ary balanced codes with fast syndrome-based error correction. IEEE Transactions on Information Theory, 64(4):2431-2443. DOI:10.1109/TIT.2017.2767034
- Description: Abstract: We investigate a Knuth-like scheme for balancing q-ary codewords, which has the virtue that look-up tables for coding and decoding the prefix are avoided by using precoding and error correction techniques. We show how the scheme can be extended to allow for error correction of single channel errors using a fast decoding algorithm that depends on syndromes only, making it considerably faster compared to the prior art exhaustive decoding strategy. A comparison between the new and prior art schemes, both in terms of redundancy and error performance, completes the study.
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- Authors: Swart, Theo G. , Weber, Jos H. , Schouhamer Immink, Kees A.
- Date: 2018
- Subjects: Balanced code , Constrained code , error correction
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/279793 , uj:30054 , Citation: Swart, T.G., Weber, J.H. & Schouhamer Immink, K.A. 2018. Prefixless q-ary balanced codes with fast syndrome-based error correction. IEEE Transactions on Information Theory, 64(4):2431-2443. DOI:10.1109/TIT.2017.2767034
- Description: Abstract: We investigate a Knuth-like scheme for balancing q-ary codewords, which has the virtue that look-up tables for coding and decoding the prefix are avoided by using precoding and error correction techniques. We show how the scheme can be extended to allow for error correction of single channel errors using a fast decoding algorithm that depends on syndromes only, making it considerably faster compared to the prior art exhaustive decoding strategy. A comparison between the new and prior art schemes, both in terms of redundancy and error performance, completes the study.
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Simple systematic pearson coding
- Weber, Jos H., Swart, Theo G., Schouhamer Immink, Kees A.
- Authors: Weber, Jos H. , Swart, Theo G. , Schouhamer Immink, Kees A.
- Date: 2016
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/123960 , uj:20857 , Citation: Weber, J.H., Swart, T.G. & Schouhamer Immink, K.A. 2016. Simple systematic pearson coding.
- Description: Abstract: The recently proposed Pearson codes offer immunity against channel gain and offset mismatch. These codes have very low redundancy, but efficient coding procedures were lacking. In this paper, systematic Pearson coding schemes are presented. The redundancy of these schemes is analyzed for memoryless uniform sources. It is concluded that simple coding can be established at only a modest rate loss.
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- Authors: Weber, Jos H. , Swart, Theo G. , Schouhamer Immink, Kees A.
- Date: 2016
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/123960 , uj:20857 , Citation: Weber, J.H., Swart, T.G. & Schouhamer Immink, K.A. 2016. Simple systematic pearson coding.
- Description: Abstract: The recently proposed Pearson codes offer immunity against channel gain and offset mismatch. These codes have very low redundancy, but efficient coding procedures were lacking. In this paper, systematic Pearson coding schemes are presented. The redundancy of these schemes is analyzed for memoryless uniform sources. It is concluded that simple coding can be established at only a modest rate loss.
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