Iterative decoding as Dykstra's algorithm with alternate I-projection and reverse I-projection

Bit interleaved Coded Modulation with iterative decoding is known to provide excellent performance over both Gaussian and fading channels. However a complete analysis of the iterative demodulation is still lacking. In this paper, we complete the geometric interpretation of turbo-like iterative demodulation and we give an interpretation for the extrinsic propagation. We prove that iterative demodulation is the Dykstra's algorithm with I-projections and reverse I-projections.