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Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design by Alex Alvarado, Leszek Szczecinski

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6.1.3 Bounding Techniques

The approach we used to evaluate the TP in 2D constellations can be extended to the general c06-math-0253-dimensional case. However, the geometric considerations get more tedious as the dimension of the integration space increases. Therefore, simple approximations are often used, which may also be sufficient for the purpose of the analysis and/or design. A popular approach relies on finding an upper bound on the TP c06-math-0254, which we do in the following.

For a given c06-math-0255, and for any c06-math-0256 with c06-math-0257, we have

6.72 equation

which follows from the fact that, by using one inequality, we relax the constraint imposed by c06-math-0259 inequalities defining c06-math-0260. The TP is therefore upper bounded, for any , as

Setting we obtain ...

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