Achievable bound An achievable rate Popularity M l]+∑K i>NI 1 Popular"“ Unpopular KM The minimum occurs at M°p11 File Index KM Proposition 1: Assume M2 2. There exists an achievable scheme whose average transmission rate satisfies R(K,F,P)≤Rb= M Kpi N Where m1 satisfies p,≥ 1 Am and pN1+1KM 12Achievable Bound • An achievable rate: • The minimum occurs at • Proposition 1: Assume 𝑀 ≥ 2. There exists an achievable scheme whose average transmission rate satisfies: 𝑅 𝐾,ℱ, 𝒫 ≤ 𝑅𝑢𝑏 = 𝑁1 𝑀 − 1 + + ෍ 𝑖>𝑁1 𝐾𝑝𝑖 where 𝑁1 satisfies 𝑝𝑁1 ≥ 1 𝐾𝑀 and 𝑝𝑁1+1 < 1 𝐾𝑀 . 12 1 1 [ 1] i i N N Kp M  − +  1 1 KpN M  File Index Popularity 1 𝐾𝑀 𝑁1 “Popular” “Unpopular” 1 1 N p KM 