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 c05-math-0317, and then, we will find the PDF of the L-values for arbitrary 2D constellations.

5.3.1 Space Tessellation

Finding the tessellation regions c05-math-0318 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 c05-math-0319QAM, the regions c05-math-0320 may significantly change in a function of the binary labeling.

We start by rewriting (5.27) as

5.67 equation
5.68 equation

where , , and is given by (3.54).

These tessellation regions are mutually ...

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