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

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

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

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

Multiple access with distance preserving mappings for permutation codes

We present results for Distance Preserving Mappings (DPMs) for permutation codes that can be used for multiple access communication even under frequency jamming. We give examples of multiple codebooks that are DPMs such that each DPM can be assigned to a user for communication over a multiple access channel. We only consider one type of DPM called Distance Increasing Mappings (DIMs). The multiple access channel of interest is Time Division Multiple Access (TDMA). We show that it is possible to give a construction for DIMs that can be uniquely decoded even in the presence of frequency jamming. The DPMs are permutation codes found by mapping binary sequences to permutation sequences. The permutation codes have codewords of length M with symbols taken from an alphabet whose cardinality is M, where M is any integer. Each symbol may be seen as representing one out of the M frequencies in an M-ary Frequency Shift keying modulation scheme, for example

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

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