New distance concept and graph theory approach for certain coding techniques design and analysis

Abstract: A New graph distance concept introduced for certain coding techniques helped in their design and analysis as in the case of distance-preserving mappings and spectral shaping codes. A graph theoretic construction, mapping binary sequences to permutation sequences and inspired from the k-cube graph has reached the upper bound on the sum of the distances for certain values of the length of the permutation sequence. The new introduced distance concept in the k-cube graph helped better understanding and analyzing for the first time the concept of distance-reducing mappings. A combination of distance and the index-permutation graph concepts helped uncover and verify certain properties of spectral null codes, which were previously difficult to analyze

An overview of outdoor visible light communications

Abstract: In visible light communications (VLC) technology, the outdoor applications are less explored when compared to those indoors. This is due to the fact that: (i) the dual use of light emitting diodes (LEDs) is not always practicable in the outdoor VLC environment; (ii) the level of interference and noise is considerably higher in outdoor VLC; (iii) many other communication technologies are available to be used which, due to their specific characteristics, adapt better to the outdoor environment when compared to VLC technology. Nevertheless, several outdoor VLC applications have been identified. They include and are not limited to building-to-building (B2B), vehicle-to-vehicle (V2V) and road-to-vehicle (R2V) communications. Deploying light fidelity (Li-Fi) using street and park lights is also feasible. Finally, some applications exploit the ability of solar panels to simultaneously harvest the electrical energy and serve as a VLC receiving antenna. The implementation of these communication systems faces lots of challenges. Most of them are related to environmental factors such as fog, rain, sunlight, haze, snow, dust, and atmospheric disturbances. Some challenges are based on parameters such as the geometrical aspect of the light diffusion, which is Lambertian in most cases. These challenges contribute to lower interest in outdoor VLC to date. However, the environment presents several opportunities. In this article, we explore the outdoor VLC environment, review and present some promising applications selected from the literature. Furthermore, we underline likely research opportunities based on the actual state-of-the-art and our outdoor VLC characterisation experiments

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

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

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

Variable- and fixed-length balanced runlength-limited codes based on a Knuth-like balancing method

Abstract: A novel Knuth-like balancing method for runlengthlimited words is presented, which forms the basis of new variableand fixed-length balanced runlength-limited codes that improve on the code rate as compared to balanced runlength-limited codes based on Knuth’s original balancing procedure developed by Immink et al. While Knuth’s original balancing procedure, as incorporated by Immink et al., requires the inversion of each bit one at a time, our balancing procedure only inverts the runs as a whole one at a time. The advantage of this approach is that the number of possible inversion points, which needs to be encoded by a redundancy-contributing prefix/suffix, is reduced, thereby allowing a better code rate to be achieved. Furthermore, this balancing method also allows for runlength violating markers which improve, in a number of respects, on the optimal such markers based on Knuth’s original balancing method

Mathematical approach and implementation of frequency mapping techniques in power-line communications channel

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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