A multilevel construction for mappings from binary sequences to permutation sequences

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

Analysis of permutation distance-preserving mappings using graphs

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

Decoding distance-preserving permutation codes for power-line communications

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

Investigation of factors governing the stability of stope panels in hard rock mines in order to define a suitable design methodology for shallow mining operations

Instability in stope panels in shallow mines manifests itself as rockfalls from the hangingwall. Rockfalls from unstable stope panels vary in size from rockfalls between support units, to rockfalls spanning between pillars or solid abutments, to rockfalls bridging several panels and pillars. A suitable and reliable design methodology for stable stope panels at shallow depths is therefore required. This methodology must consider all manifestations of instability in stope panels and take account of the factors governing the stability. Very few mines design stope panels according to a systematic design procedure or methodology. Rock mass characterisation, estimation of rock mass properties, identification of potential failure modes, appropriate stability analyses and other elements of the rock engineering design process are often neglected. Instead, panel lengths are often dictated by the equipment in use and by previous experience under similar conditions. Consequently, unplanned stope panel collapses occur on most near-surface and shallow mines. Although these incidents often occur during blasting, they pose a major threat to the safety of underground workers and the economic extraction of orebodies. Hence, a rock engineering design methodology for the design of stable stope panels between pillars is of vital importance for optimum safety and production in shallow mining operations. Using the proposed design methodology, rock mechanics practitioners and mine planners should be able to identify and quantify the critical factors influencing the stability of stope panels. The critical factors should then be used as input to the design of stable stope panels that will provide the necessary safe environment for underground personnel working in stopes. It is concluded that the design of stable stope panels should be a process of defining the means of creating stable stope panels for the safety of underground workers and optimum extraction of the orebody. Therefore, a method is required whereby all rock properties, their variability, and an understanding of all rock mechanisms affecting the stability of stope spans are used as a fundamental base. A procedure for identifying the mechanisms and rock properties relevant to the specific problem is then required. In this way, existing knowledge should be used in an optimal way to design site specific stable stope spans. Hence, it is proposed that the design methodology for stable stope panels is a process consisting of the following steps: 1. Define objective. 2. Rock mass characterisation. 3. Estimation of in situ rock mass properties. 4. Consider an “ideal” stope panel. 5. Identification of potential failure modes. 6. Stability analyses. 7. Identify all significant hazards and assess the significant risks. 8. Geometric optimisation. 9. Determination of support requirements. 10. Design of support. 11. Evaluation. 12. Recommendation and implementation. 13. Monitoring of excavation and support behaviour to validate design and permit modifications.Dissertation (MEng (Mining))--University of Pretoria, 2006.Mining Engineeringunrestricte

Combined permutation codes for synchronization

Abstract: A combined code is a code that combines two or more characteristics of other codes. A construction is presented in this paper of permutation codes that are self-synchronizing and able to correct a number of deletion errors per codeword, thus a combined permutation code. Synchronization errors, modelled as deletion(s) and/or insertion(s) of bits or symbols, can be catastrophic if not detected and corrected. Some classes of codes have been proposed that are synchronizable, i.e. they can be used to regain synchronization although the error leading to the loss of synchronization is not corrected. Typically, different classes of codes are needed to correct deletion and/or insertion errors after codeword boundaries have been detected. The codebooks presented in this paper consist of codewords divided into segments. By imposing restrictions on the segments, the codewords are synchronizable. One deletion error can be detected and corrected per segment

Re-synchronization of permutation codes with Viterbi-like decoding

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

Binary permutation sequences as subsets of Levenshtein codes and higher order spectral nulls codes

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

Synchronization using insertion/deletion correcting permutation codes

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

Using graphs for the analysis and construction of permutation distance-preserving mappings

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