The L-values are the signals/messages exchanged in bit-interleaved coded modulation (BICM) receivers. We saw in Chapter 3 that, thanks to the formulation of the L-values in the logarithm domain, multiplication of probabilities/likelihoods transforms into addition of the corresponding L-values. This makes the L-values well suited for numerical implementation. Furthermore, the L-values can be processed in abstraction of how they were calculated. The designer can then connect well-defined processing blocks, which is done under the assumption that the L-values can be transformed into probabilities/likelihoods. This assumption does not hold in all cases, as the L-values might have been incorrectly calculated, resulting in mismatched L-values. In this chapter, we take a closer look at the problem of how to deal with this mismatch.
We will discuss the motivation for L-values correction in Section 7.1 and explain optimal processing rules in Section 7.2. Suboptimal (linear) correction strategies will be studied in Section 7.3.
As discussed in Section 3.2, the BICM decoding rule
is solely based on the L-values calculated as
Thus, decoding is carried out in abstraction of the channel model, i.e., ...