Simulation results for permutation trellis codes using M-ary FSK
- Authors: Swart, Theo G. , De Beer, I. , Ferreira, Hendrik C. , Han Vinck, A. J.
- Date: 2005
- Subjects: Channel coding , Convolutional codes , Interference suppression
- Language: English
- Type: Conference proceedings
- Identifier: http://ujcontent.uj.ac.za8080/10210/368327 , http://hdl.handle.net/10210/18512 , uj:16008 , Citation: Swart, T.G. et al. 2005. Simulation results for permutation trellis codes using M-ary FSK. Proceedings of the IEEE International Symposium on Power Line Communications and its Applications, 6-8 April, 2005, Vancouver, Canada.
- Description: Abstract: It has previously been shown that using the combination of permutation codes and M-ary frequency shift keying has special properties and error correcting capabilities that are suitable for the noise types encountered in power line communications. Furthermore, the permutation codes are used to map onto the outputs of a binary convolutional code to form permutation trellis codes. We investigate and compare the performance of different permutation trellis codes when used with M-FSK for power line communications.
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A multilevel construction for mappings from binary sequences to permutation sequences
- Authors: Swart, Theo G. , Ferreira, Hendrik C.
- Date: 2006
- Subjects: Mappings , Binary sequences , Permutation sequences
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/18365 , uj:15991 , Citation: Swart, T.G. & Ferreira, H.C. 2006. A multilevel construction for mappings from binary sequences to permutation sequences. Proceedings of the IEEE International Symposium on Information Theory, 9-14 July, 2006, Seattle, USA.
- Description: Abstract: A multilevel construction is introduced to create distance-preserving mappings from binary sequences to permutation sequences. It is also shown that for certain values, the new mappings attain the upper bound on the sum of Hamming distances obtainable for such mappings, and in the other cases improve on those of previous mappings.
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Binary permutation sequences as subsets of Levenshtein codes and higher order spectral nulls codes
- Authors: Ouahada, Khmaies , Swart, Theo G. , Ferreira, Hendrik C.
- Date: 2006
- Subjects: Levenshtein codes , Spectral nulls codes , Binary permutation sequences
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/18858 , uj:16051 , Citation: Ouahada, K., Swart, T.G. & Ferreira, H.C. 2006. Binary permutation sequences as subsets of Levenshtein codes and higher order spectral nulls codes. Proceedings of IEEE Information Theory Workshop, Chengdu, 22-26 October, 2006, China, October.
- Description: Abstract: We obtain long binary sequences by concatenating the columns of (0,1)-matrices derived from permutation sequences. We then prove that these binary sequences are subsets of the Levenshtein codes, capable of correcting insertion/deletion errors and subsets of the higher order spectral nulls codes, with spectral nulls at certain frequencies.
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Insertion/deletion correction by using parallel-interconnected viterbi decoders
- Authors: Swart, Theo G. , Ferreira, Hendrik C. , Dos Santos, M. P. F.
- Date: 2006
- Subjects: Error-correcting codes (Information theory) , Coding theory , Synchronization
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/21161 , uj:16118 , Citation: Swart, T.G., Ferreira, H.C. & Dos Santos, M.P.F. 2006. Insertion/deletion correction by using parallel interconnected viterbi decoders. South African Institute of Electrical Engineers, 97(2):151-156.
- Description: Abstract: A new insertion/deletion correction scheme is presented for standard convolutional codes that makes use of multiple parallel-interconnected Viterbi decoders. Whenever an insertion or deletion error occurs, the connections between different Viterbi decoders ensure that decoding will proceed from the decoder that is in synchronization . In this way, a larger Viterbi decoder is created that can correct insertion and/or deletion errors by extending the Viterbi algorithm to encompass all parallel decoders. Further, it is shown how the performance can be improved by inverting certain bits during the encoding of the convolutional codes. This lowers the frequency of occurrence of repeating sequences, which is detrimental to synchronization when dealing with insertions/deletions.
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An analogue to SNR for timing synchronisation motivated by jitter and insertion/deletion errors
- Authors: Paluncic, Filip. , Clarke, Willem A. , Swart, Theo G. , Ferreira, Hendrik C.
- Date: 2007
- Subjects: Signal-to-noise ratio , Timing jitter , Insertion/deletion errors
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/15424 , uj:15659 , Citation: Paluncic, F. et al. 2007. An analogue to SNR for timing synchronisation motivated by jitter and insertion/deletion errors. In: Proceedings of the International Symposium on Communication Theory and its Applications, Ambleside, England, July 16-20, 2007.
- Description: Abstract: This paper takes a closer look at the relationship between insertion/deletion errors and one of its most common causes, timing jitter. We consider two insertion/deletion channel models based on different assumptions about the timing jitter. In the literature, only channels with equal insertion/deletion probabilities for each bit have been considered. However, this assumption is only true under certain conditions. A channel, where the probability of insertion/deletion errors increases with time, is another feasible scenario. We derive an approximation for the probability of insertion/deletion errors for both models. With these ideas, we also define a possible counterpart in the time domain to the signal-to-noise ratio (defined in the amplitude domain). As an analogue to Gaussian noise in the amplitude domain, we only consider random Gaussian distributed jitter.
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Analysis of permutation distance-preserving mappings using graphs
- Authors: Swart, Theo G. , Ferreira, Hendrik C.
- Date: 2007
- Subjects: Mappings (Mathematics) , Permutations , Representations of graphs
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/15518 , uj:15670 , Citation: Swart, T.G. & Ferreira, H.C. 2007. Analysis of permutation distance-preserving mappings using graphs. In: Proceedings of the International Symposium on Communication Theory and its Applications, Ambleside, England, July 16-20, 2007
- Description: Abstract A new way of analyzing permutation distance preserving mappings is presented by making use of a graph representation. The properties necessary to make such graphs distance-preserving and how this relates to the total sum of distances that exist for such mappings, are investigated. This new knowledge is used to analyze previous constructions, as well as showing the existence or non-existence of simple algorithms for mappings attaining the upper bound on the sum of distances. Finally, two applications for such graphs are considered.
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Cancellation and error correction for narrowband interference with spectral nulls codes and OFDM modulation
- Authors: Ouahada, K. , Ferreira, Hendrik C. , Han Vinck, A. J. , Snyders, A. J. , Swart, Theo G.
- Date: 2007
- Subjects: Error-correcting codes (Information theory) , Spectral nulls codes
- Language: English
- Identifier: http://hdl.handle.net/10210/18135 , uj:15964 , Citation: Ouahada, K. et al. 2007. Cancellation and error correction for narrowband interference with spectral nulls codes and OFDM modulation. Proceedings of IEEE Africon, 26-28 September, 2007, Windhoek, Namibia.
- Description: Conference proceedings
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Convolutional code search for optimum permutation trellis codes using M-ary FSK
- Authors: Swart, Theo G. , Han Vinck, A. J. , Ferreira, Hendrik C.
- Date: 2007
- Subjects: Channel coding , Permutation codes , Frequency-shift keying , Interference suppression
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/18537 , uj:16011 , Citation: Swart, T.G., Vinck, A.J.H. & Ferreira, H.C. 2007. Convolutional code search for optimum permutation trellis codes using M-ary FSK. Proceedings of the IEEE International Symposium on Power Line Communications and its Applications, 26-28 March, 2007.
- Description: Abstract: Permutation trellis codes combined with M-ary FSK are considered with the aim of combating additive noise, impulse noise and permanent frequency disturbances. New permutation trellis codes are presented that were found by exhaustive computer search, considering the free distance and the distance spectrum of the codes. Until now the best binary convolutional codes were considered to be the best candidates to use in mappings for trellis codes, however the results will show that this is not always the case. Simulation results are also presented, showing that in most cases the new permutation trellis codes are performing better than the previous codes, although the gains attained are small.
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Decoding distance-preserving permutation codes for power-line communications
- Authors: Swart, Theo G. , Ferreira, Hendrik C.
- Date: 2007
- Subjects: Distance-preserving , Permutation codes , Power-line communications
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/17971 , uj:15943 , Citation: Swart, T.G. & Ferreira, H.C. 2007. Decoding distance-preserving permutation codes for power-line communications. Proceedings of IEEE Africon, 26-28 September, 2007, Windhoek, Namibia.
- Description: Abstract: A new decoding method is presented for permutation codes obtained from distance-preserving mapping algorithms, used in conjunction with M-ary FSK for use on powerline channels. The new approach makes it possible for the permutation code to be used as an inner code with any other error correction code used as an outer code. The memory and number of computations necessary for this method is lower than when using a minimum distance decoding method.
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Decoding distance-preserving permutation codes for power-line communications
- Authors: Swart, Theo G. , Ferreira, Hendrik C.
- Date: 2007
- Subjects: Power-line communications , Permutation codes , Decoding methods
- Language: English
- Type: Conference paper
- Identifier: http://hdl.handle.net/10210/165801 , uj:15452 , T. G. Swart and H. C. Ferreira, "Decoding distance-preserving permutation codes for power-line communications," in Proceedings of IEEE Africon, Windhoek, Namibia, September 26-28, 2007, published on CD (6 pages).
- Description: A new decoding method is presented for permutation codes obtained from distance-preserving mapping algorithms, used in conjunction with M-ary FSK for use on powerline channels. The new approach makes it possible for the permutation code to be used as an inner code with any other error correction code used as an outer code. The memory and number of computations necessary for this method is lower than when using a minimum distance decoding method.
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Error correction of frequency-selective fading channels with spectral nulls codes
- Authors: Ouahada, K. , Ferreira, Hendrik C. , Snyders, A. J. , Han Vinck, A. J. , Swart, Theo G.
- Date: 2007
- Subjects: Frequency-selective fading channels , Spectral nulls codes
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/18126 , uj:15962 , Citation: Ouahada, K. et al. 2007. Error correction of frequency-selective fading channels with spectral nulls codes. Proceedings of IEEE Africon, 26-28 September, 2007, Windhoek, Namibia.
- Description: Abstract: In this paper, we investigate a prior error correction technique for frequency selective fading channels. Spectral nulls codes with nulls at submultiple frequencies are used to avoid fades at the corresponding frequencies. Coincide the spectrum null at the corresponding fading frequency and playing with its wideness, will minimize the bit errors caused by the channel.
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Moment balancing templates: Universal constructions to add insertion/deletion correction capability to arbitrary error correcting or constrained codes
- 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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New DC-free multilevel line codes with spectral nulls at rational submultiples of the symbol frequency
- Authors: Ouahada, Khmaies , Ferreira, Hendrik C. , Swart, Theo G.
- Date: 2007
- Subjects: Multilevel line codes , Spectral nulls
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/15647 , uj:15684 , Ouahada, K., Ferreira, H.C. & Swart, T.G. 2007. New DC-free multilevel line codes with spectral nulls at rational submultiples of the symbol frequency. Proceedings of the International Symposium on Communication Theory and its Applications, 16-20 July, Ambleside, England.
- Description: Abstract A new technique of designing multilevel line codes is presented. Distance-preserving mappings from binary sequences to permutation sequences are used, where the permutation sequences also have spectral nulls properties. The resultant line codes use the structure of the convolutional codes and thus have certain advantages compared to other published line codes.
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Binary permutation sequences as subsets of Levenshtein codes, spectral null codes, run-length limited codes and constant weight codes
- Authors: Ouahada, Khmaies , Swart, Theo G. , Ferreira, Hendrik C. , Cheng, Ling
- Date: 2008
- Subjects: Permutation codes , Insertion/deletion correcting codes , Constant weight codes , Spectral null codes , Run-length limited codes
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/18337 , uj:15986 , Citation: Ouahada, K. et al. 2008. Binary permutation sequences as subsets of Levenshtein codes, spectral null codes, run-length limited codes and constant weight codes. Designs, Codes and Cryptography, 48(2): 141-154. DOI: 10.1007s10623-007-9161-7. , DOI: 10.1007s10623-007-9161-7.
- Description: Abstract: We investigate binary sequences which can be obtained by concatenating the columns of (0,1)-matrices derived from permutation sequences. We then prove that these binary sequences are subsets of a surprisingly diverse ensemble of codes, namely the Levenshtein codes, capable of correcting insertion/deletion errors; spectral null codes, with spectral nulls at certain frequencies; as well as being subsets of run-length limited codes, Nyquist null codes and constant weight codes.
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Combined spectral shaping codes and OFDM modulation for narrowband interference channels
- Authors: Ouahada, K. , Ferreira, Hendrik C. , Han Vinck, A. J. , Snyders, A. J. , Swart, Theo G.
- Date: 2008
- Subjects: Distance-preserving mappings , Spectral nulls codes , Spectral shaping codes , OFDM modulation , Narrowband interference
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/21215 , uj:16126 , Citation: Ouahada, K. et al. 2008. Combined spectral shaping codes and OFDM modulation for narrowband interference channels. SAIEE Africa Research Journal, 99(1):11-17.
- Description: Abstract: Distance Preserving Mappings is a relatively new technique finding its way to a wide use in the coding field. New codes mapping convolutional code outputs onto spectral nulls codewords have the purpose of generating a code with a certain spectrum specification and error correction capabilities, which can be exploited by the Viterbi decoder. Combining this class of new codes with an Orthogonal Frequency Division Multiplexing modulation scheme is actually a tool to reduce Electromagnetic Compatibility Interference in selected subbands or to cancel the narrowband interference potentially caused by, amongst others, high frequency radio transmissions. Taking into consideration the fact that a narrowband noise source is almost similar to a modulated orthogonal frequency division multiplexing carrier, and also the periodicity of the nulls in our spectrum, we are able to cancel the narrowband signal and its sideband interferences without using traditional techniques of cancellation, which is based on filtering. Shaping our spectrum at the transmitter is a technique, which can be exploited at the receiver to suppress any narrowband signal interference, which is regarded as noise. We will present in this paper the technique of cancellation and the coding gain that can be obtained when comparing to the uncoded data.
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Synchronization using insertion/deletion correcting permutation codes
- Authors: Cheng, Ling , Swart, Theo G. , Ferreira, Hendrik C.
- Date: 2008
- Subjects: Synchronization , Permutation codes
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/18690 , uj:16031 , Citation: Cheng, L., Swart, T.G. & Ferreira, H.C. 2008. Synchronization using insertion/deletion correcting permutation codes. Proceedings of the IEEE International Symposium on Power Line Communications and its Applications, 2-4 April, 2008, Jeju City, Jeju Island, South Korea.
- Description: Abstract: In this paper, we present a fast synchronization coding scheme, which uses single insertion/deletion error correcting permutation codes. A possible application to M-ary FSK for the CENELEC A band power-line communications (PLC) is considered. Compared to conventional timing recovery schemes, no redundancies for preamble sequences and no processing delays from decision devices are needed.
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Using graphs for the analysis and construction of permutation distance-preserving mappings
- Authors: Swart, Theo G. , Ferreira, Hendrik C. , Ouahada, Khmaies
- Date: 2008
- Subjects: Code construction , Distance-preserving mappings , Representation of graphs , Permutations , Mappings (Mathematics)
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/20030 , uj:16060 , ISSN: 0018-9448 , Citation: Swart, T.G., Ferreira H.C. & Ouahada, K. 2008. Using graphs for the analysis and construction of permutation distance-preserving mappings. IEEE Transactions on Information Theory, 54(2):910-916.
- Description: Abstract: A new way of looking at permutation distance-preserving mappings (DPMs) is presented by making use of a graph representation. The properties necessary to make such a graph distance-preserving, are also investigated. Further, this new knowledge is used to analyze previous constructions, as well as to construct a new general mapping algorithm for a previous multilevel construction.
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Modelling distances between genetically related languages using an extended weighted Levenshtein distance
- Authors: Paluncic, F. , Ferreira, Hendrik C. , Swart, Theo G. , Clarke, W. A.
- Date: 2009
- Subjects: Levenshtein distance , Insertion/deletion
- Language: English
- Type: Abstract
- Identifier: http://hdl.handle.net/10210/21309 , uj:16139 , ISSN: 1607-3614 , DOI: 10.2989/SALALS.2009.27.4.2.1022 , Citation: Paluncic, F. et al. 2009. Modelling distances between genetically related languages using an extended weighted Levenshtein distance. Southern African Linguistics and Applied Language Studies Journal, 27(4):381-389. DOI: 10.2989/SALALS.2009.27.4.2.1022.
- Description: Abstract: This article proposes the use of an extended weighted Levenshtein distance to model the time depth between parent and direct descendant languages and also the dialectal separation between sibling languages. The parent language is usually a proto-language, a hypothetical reconstructed language, whose precise date is usually conjectural. Phonology is used as an indicator of language difference, which is modelled by means of an extended weighted Levenshtein distance. This idea is applied specifically to the Iranian language family.
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Moment balancing templates: constructions to add insertion/deletion correction capability to error correcting or constrained codes
- 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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Re-synchronization of permutation codes with Viterbi-like decoding
- Authors: Cheng, Ling , Swart, Theo G. , Ferreira, Hendrik C.
- Date: 2009
- Subjects: Synchronization , Permutation codes , Decoding
- Language: English
- Type: Conference proceedings
- Identifier: http://hdl.handle.net/10210/18809 , uj:16045 , ISBN: 978-1-4244-3790-0 , Citation: Cheng, L., Swart, T.G. & Ferreira, H.C. 2009. Re-synchronization of permutation codes with Viterbi-like decoding. Proceedings of the IEEE International Symposium on Power Line Communications and its Applications, 29 March - 1 April, 2009, Dresden, Germany.
- Description: Abstract: In this paper, we present a fast re-synchronization algorithm for permutation coded sequences. The new algorithm combines the dynamic algorithm and a Viterbi-like decoding algorithm for trellis codes. The new algorithm has a polynomial time complexity O(N), where N denotes the length of the sequence. A possible application to M-ary FSK for the CENELEC A band power-line communications (PLC) is considered.
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