Page 118 - ISCI’2017

the ITS space. For example, at n = 24 there is the densest packing based on the Leech lattice and

built with the Golay binary code [10, 11], in which the surface of one sphere is adjoined by 196560
surrounding spheres. If on the basis of this lattice any redundant(24,k ) -codes with k 1,2,=  ,18 ,

are constructed, it will be possible to provide mutual equidistance between all signal (code) points.
Even if channel capacity is exceeded insignificantly (small overlapping of the uncertainty spheres),

reception of any codeword on the channel output on the basis of MLR is almost equiprobable and
practically independent from the transmitted word (message). In such conditions maximum likelihood

rule usage certainly leads to an error in the reception. Therefore, there is a paradox and contradiction:
on the one hand, MLR is the best way to receive, which minimizes the probability of errors at a low

noise; on the other hand – the rule itself is the cause of limitations on the permissible rate and/or noise

power. Can the decision-making rule be modified when we use encoding and probabilistic estimation
of the channel output state?

118