Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design

Chapter 7Correction of L-values

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.

7.1 Mismatched Decoding and Correction of L-values

As discussed in Section 3.2, the BICM decoding rule

7.1

is solely based on the L-values calculated as

7.2

Thus, decoding is carried out in abstraction of the channel model, i.e., ...