Om potentialen för permutationsbaserad repetitionskodning-liknande symbolnivå kodning

Linus Larsson ()

Sammanfattning

The purpose of this thesis is to investigate the potential of transmitting data
symbols alongside permuted copies in a repetition coding-like scheme, called the
permutation scheme. First exhaustive search is conducted for small constellation
sizes to identify possible patterns. The next step consisted of identifying local
search methods for permutations, and other methods for entire combinations of
permutations. It was found that as permutations are used, the energy efficiency
of the high-dimensional constellation improves as more and more permutations are used.
It was also found that the union bound of a high-dimensional constellation is still
indicative of the constellations respective bit error ratio performance. Note that
for the bit error ratio these results stem from a simplistic simulation where the
only factor considered was additive white Gaussian noise. Another seminal 
investigation was if, and how the permutation scheme could be used alongside binary 
coding schemes such as block codes and random interleaving. The results show that 
the block codes do work in conjunction with the permutation scheme, and that random 
interleaving still functions as expected. Another property of permutations that was 
examined is how optimal permutations for 8-PSK constellations were affected when 
the constellation points are normalized with their respective p-norms. The results 
suggest that infinity norm permutations have some innate qualities not found 
in every 2-norm permutation