A Monte Carlo simulation program for the radio detection of Ultra High Energy (UHE) neutrino interactions in the Antarctic ice as viewed by the Antarctic Impulsive Transient Antenna (ANITA) is described in this article. The program, icemc, provides an input spectrum of UHE neutrinos, the parametrization of the Askaryan radiation generated by their interaction in the ice, and the propagation of the radiation through ice and air to a simulated model of the third and fourth ANITA flights. This paper provides an overview of the icemc simulation, descriptions of the physics models used and of the ANITA electronics processing chain, data/simulation comparisons to validate the predicted performance, and a summary of the impact of published results.
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