function z_hat = babai(R,y)
%%
%   compute the Babai estimation
%   find a sub-optimal solution for min_z ||R*z-y||_2
%   R - an upper triangular real matrix of n-by-n
%   y - a real vector of n-by-1
%   z_hat - resulting integer vector
%
    n=length(y);
    z_hat=zeros(n,1);
    z_hat(n)=round(y(n)./R(n,n));
    for k=n-1:-1:1
        par=R(k,k+1:n)*z_hat(k+1:n);
        ck=(y(k)-par)./R(k,k);
        z_hat(k)=round(ck);
    end

end