Disclosed are methods and structures for soft symbol and variance estimation for QAM constellations including a big-flipping framework and efficient methods for soft symbol estimation and variance estimation for QAM. Disclosed are efficient Gray mapping which provides a much lower complexity, i.e., log N for N-QAM for both squared and non-squared QAM constellations. Also disclosed is an approximation method that avoids multiplications completely while exhibiting only a slight performance degradation. Finally, a low complexity method for variance estimations, particularly second moment estimations for both squared and non-squared QAM constellations with Gray mapping are disclosed. Advantageously—using the disclosed methods—the complexity of the second moment estimation is reduced to O((log N)^2) for an N-QAM symbol for both squared and non-squared QAM.