First-order sigma-delta ADC quantization noise cancellation
First, the 1/2 factor at the input is superfluous; it has no useful  function. Second, you seem to have an ADC that is able to reproduce an exact version of its input signal.  This is not possible since an ADC only has a finite number of output values while the input analog signal can have an infinite number of values since it is a continuous function.  This means that different input signals can map to the same ADC output due to the finite quantization of the ADC. Thus once you have done an ADC conversion, you have lost some information about the input signal.  Therefore you cannot reproduce it exactly at the output. Therefore I believe there is a fundamental flaw in your design. As suggested by Andy, try simulating it and see what happens especially with different types of input signals: sine, square and triangle.