Binary symmetric channel is just flipping bits with a certain probability.
x = [1, 1, 0, 0, 0, 0, 0, 0, 1, 1];
p = 0.1; % with probability p, make an error
errorbits = rand(size(x)) < p; % toss some biased coins and make a logical index
y = x; % first perfectly copy
y(errorbits) = 1 - y(errorbits); % make 0 -> 1 and 1 -> 0
Do you see how this is a $P(y|x)$ that implements the symmetric binary channel?