From the results in Sections 6.2.4 and 6.2.5, we know that finding the PEP in (6.166) and (6.226) is instrumental to evaluate the performance of the ML and BICM decoders, respectively. In the case of the BICM decoder we need to evaluate

where

and is the average PDF given in (6.227). Alternatively, we might want to calculate

where

and carry out the summation (6.233) over . Note that, to simplify the notation we removed the subindexing with we used in (6.210).

Although we used the same notation in (6.283) and (6.285), the random variables described by these PDFs are not the same. In the first case, to evaluate the PEP, we have to consider only ...

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