The analysis shown in Section 5.2 is slightly more involved in the case of 2D constellations. In what follows, we will first describe how to find the tessellation regions , and then, we will find the PDF of the L-values for arbitrary 2D constellations.
Finding the tessellation regions for 1D constellations is relatively simple and can be done by inspection, as we did, e.g., in Example 5.5. A more structured approach is required for 2D constellations, because as we will see, even with very regular constellations such as QAM, the regions may significantly change in a function of the binary labeling.
We start by rewriting (5.27) as
where , , and is given by (3.54).
These tessellation regions are mutually ...