You can pass an cell array of strings to the legend() (here for documentation https://de.mathworks.com/help/matlab/ref/legend.html) function in order to have what you want. For this just initialize an array before and then, for each interation, save the string that you want to be shown (I change your inner loop index so it is not the same i as the outer loop):
sample=10000;
s = -1 + (2).*rand(sample,1);
s = nonzeros(s);
s(s<0)=-1;
s(s>0)=1;
change_a=0.2:0.2:2
variance_a=sqrt(change_a)*(1/12)
LegendsStrings = cell(length(change_a),1); % Initialize array with legends
for i=1:length(change_a)
%Define Channel
change_n=0:0.2:2;
a=change_a(i)*rand(sample,1);
n=change_n.*randn(sample,1);
%channel output
y=a.*s+n;
%Define received signal as negative y equals -1 and positive y equals 1
z=y;
z(y<0)=-1;
z(y>0)=1;
%compare source signal to received signal
c=z==s;
for ii=1:size(z,2)
errors(ii)=size(z,1)-nnz(c(:,ii));
error_percent=errors./(size(z,1))*100.
end
%plot for each value of change_a a line
plot(var(n),error_percent)
xlabel('variance noise')
ylabel('error percentage')
hold on
% Save legend entry
LegendsStrings{i} = ['variance_a = ',num2str(variance_a(i))];
end
legend(LegendsStrings, 'Interpreter', 'none') % To be able to show _a
