Exploiting the Unexploited of Coded Caching for Wireless Content Distribution: Detailed Theoretical Proofs

F (qiM) (1− qiM) . Since |U/{k}| = k − 1 , the expected size of Vk,U/{k} is F (qiM) (1 − qiM) . Note that, for F large enough, the actual realization of random number of bits in Vk,S/{k} is in the interval F (qiM) (1 − qiM) K−k+1 ± o(F ), with high probability. For simplicity, the o(F ) term is ignored in the following derivation. Consider a fixed value of s in Line 7 and a fixed subset S of cardinality s. In line 8, server sends