Our research is focused on mapping binary sequences to permutation sequences. It is established that an upper bound on the sum of the Hamming distance for all mappings exists, and this sum is used as a criterion to ascertain how good previously known mappings are. We further make use of permutation trellis codes to investigate the performance of certain permutation mappings in a power-line communications system, where background noise, narrow band noise and wide band noise are present. A new multilevel construction is presented next that maps binary sequences to permutation sequences, creating new mappings for which the sum of Hamming distances are greater than previous known mappings. It also proved that for certain lengths of sequences, the new construction can attain our new upper bound on the sum of Hamming distances. We further extend the multilevel construction by showing how it can be applied to other mappings, such as permutations with repeating symbols and mappings with nonbinary inputs. We also show that a subset of the new construction yields permutation sequences that are able to correct insertion and deletion errors as well. Finally, we show that long binary sequences, formed by concatenating the columns of binary permutation matrices, are subsets of the Levenshtein insertion/deletion correcting codes. / Prof. H. C. Ferreira
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uj/uj:10062 |
| Date | 27 June 2008 |
| Creators | Swart, Theo G. |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Thesis |
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