5.3 PDF of L-values for 2D Constellations
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.
5.3.1 Space Tessellation
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 ...