Achievable Bound ·An achievable rate: Popularity ,-+∑Kp, M 1 “Popular'”“Unpopular'” KM The minimum occurs at N1 File 1 1 Index ≈KpN→PN≈ M KM Proposition 1:Assume M 2.There exists an achievable scheme whose average transmission rate satisfies: RKFm三R=贷-小+2m, where Mi satisfies PNKM and pN<M 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 