Using the relation <math>y_{i-1} XOR\oplus x_i = y_i</math> is not the only way of carrying out differential encoding. More generally, it can be any function <math>u=F(y,x)</math> provided that an equation <math>u_0=F(y_0,x)</math> has one and only one solution for any <math>y_0</math> and <math>u_0</math>.