Lower bound: statement Proposition 2: Assume thatM> 3. Let N, be the least popular file with popularity no smaller than亠,ie KM' PN1-KM and PN+1 KM For all possible coded caching schemes the average transmission rate is lower bounded by R(K,FP)≥ 1M1+N2 i>n pi 11M 2/ KM Popularity Popularity ocular Decrease Merge KM File N File N, N File Index Index Index,3Proposition 2: • Assume that 𝑀 ≥ 3. Let 𝑁1 be the least popular file with popularity no smaller than 1 𝐾𝑀 , i.e., 𝑝𝑁1 ≥ 1 𝐾𝑀 and 𝑝𝑁1+1 < 1 𝐾𝑀 . • For all possible coded caching schemes, the average transmission rate is lower bounded by 𝑅 𝐾,ℱ, 𝒫 ≥ 1 11 𝑁1 + 𝑁2 𝑀 − 1 + 13 Lower Bound: Statement File Index Popularity 1 𝐾𝑀 𝑁1 File Index Popularity 𝑁1 Decrease File Index Popularity 𝑁1 Merge 𝑁2 𝑁2 = σ𝑖>𝑁1 𝑝𝑖 2/𝐾𝑀 + 1 2