Several studies dealing with iterative Linear Minimum Mean Square Error Interference Cancellation (LMMSEIC) algorithms have concluded that better performances are obtained when soft interference cancellation is performed using Log a Posteriori Probability Ratios (LAPPRs) on coded bits rather than Log Extrinsic Probability Ratios (LEXTPRs) on coded bits. While LMMSE-IC can be rigorously derived and analyzed when it is based on LEXTPRs, things become more complicated when it relies on LAPPRs. The aim of this paper is twofold: (1) Emphasize the underlying assumptions needed for the derivation of (iterative) LAPPR based LMMSE-IC, (2) Propose an improved performance prediction method (or physical layer abstraction) robust when these assumptions do not hold. The latter contribution is a cornerstone for cross-layer design and optimization in presence of advanced turbo receivers in 3GPP.