On the symbol error probability of regular polytopes
Erik Agrell, Magnus Karlsson
TL;DR
This paper derives exact and numerically stable expressions for the symbol error probability of the 24-cell and other regular convex polytopes in Gaussian noise, aiding in performance analysis of such geometries.
Contribution
It provides the first exact formulas for these polytopes' error probabilities and summarizes their expressions, including stable numerical implementations.
Findings
Exact error probability for the 24-cell in Gaussian noise.
Summarized expressions for other regular convex polytopes.
Numerically stable versions of the error probabilities.
Abstract
An exact expression for the symbol error probability of the four-dimensional 24-cell in Gaussian noise is derived. Corresponding expressions for other regular convex polytopes are summarized. Numerically stable versions of these error probabilities are also obtained.
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