Interference cancellation circuitry is provided for reconstructing a wirelessly transmitted modulated signal in a receiver using output of a decoder for calculating per-bit probabilities corresponding to bit-by-bit estimates of a coded message from which one bit hard decisions and multi-bit soft decision can be derived. A soft modulator reconstructs the transmitted modulated signal by calculating a weighted superposition depending upon the hard decisions and at least one combined value computed by combining two or more of the multi-bit soft decisions corresponding to different bits of the coded message. A soft modulation method using combined value(s) in a weighted superposition of hard decisions and computer program code for calculating the combined values and regenerated modulated signal are also provided. Other embodiments may be described and claimed.