Exact Evaluation of Total Variation Distance in Covert Communications

This paper investigates the parameters of covert communications in a finite blocklength regime. The optimal hypothesis test in covert communications is directly related to the total variation distance (TVD), where obtaining it becomes crucial when practical covert communication is considered. The current literature provides different TVD calculation methods that are inaccurate, especially when the blocklength n is large. We provide an exact evaluation for TVD theoretically based on the incomplete Gamma function. We also provide an accurate approach to calculate TVD when n is small (n ≤ 140). Extensive numerical results were provided to verify the accuracy of our proposed expressions.