For presentational purposes, it is advisable to concentrate at the first reading of this section on the binary case where the symbols sent through a channel are 0 and 1.
As we saw earlier, in the case of an MBSC with the row error-probability p ∈ (0,1/2), the ML decoder looks for a codeword that has the maximum number of digits coinciding with the received binary word y(N). In fact, if y(N) is received, the ML decoder compares the probabilities
for different binary codewords x(N). Here
is the so-called Hamming distance between words ...