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length) increases, tends to unity monotonically.
When R < C – the probability of error can became arbitrarily small with the corresponding
n
increase of . This result can be explained by the properties of multidimensional spheres, namely,
almost all their volume is concentrated in a small area adjacent to the surface. In this area surrounding
immediately the surface of the auxiliary sphere, PDF (defined by the expression (59)) reaches its
highest values. Therefore, when the dimension of the space increases, the effective volume of layers
around of the auxiliary sphere grows faster than the density of the field of points decreases. Certainly,
we can try to formulate other criteria and decision-making rules, but, obviously, the results will be no
better than the result of the MLR (Cramer's theorem). On the basis of the conducted simulation, it is
possible to make an unambiguous conclusion – the MLR is the best and the only acceptable rule of
statistical solutions for the codes – there are no alternatives to it.
Fig. 8 – The dependencies Per(n) when using RSU and different rates
(1 → R = 1,05∙C; 2 → R = 0,95∙C; 3 → R = 0,8∙C;
4 → R = 0,7∙C; 5 → R = 0,6∙C; 6 → R = 0,5∙C)
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