New Order-Optimal Decentralized Coded Caching Schemes with Good   Performance in the Finite File Size Regime
  A decentralized coded caching scheme based on independent random content placement has been proposed by Maddah-Ali and Niesen, and has been shown to achieve an order-optimal memory-load tradeoff when the file size goes to infinity. It was then successively shown by Shanmugam et al. that in the practical operating regime where the file size is limited such scheme yields much less attractive load gain. In this paper, we propose a decentralized random coded caching scheme and a partially decentralized sequential coded caching scheme with different coordination requirements in the content placement phase. The proposed content placement and delivery methods aim at ensuring abundant coded-multicasting opportunities in the content delivery phase when the file size is finite. We first analyze the loads of the two proposed schemes and show that the sequential scheme outperforms the random scheme in the finite file size regime. We also show that both our proposed schemes outperform Maddah-Ali--Niesen's and Shanmugam et al.'s decentralized schemes for finite file size, when the number of users is sufficiently large. Then, we show that our schemes achieve the same memory-load tradeoff as Maddah-Ali--Niesen's decentralized scheme when the file size goes to infinity, and hence are also order optimal. Finally, we analyze the load gains of the two proposed schemes and characterize the corresponding required file sizes. 
Sian Jin, Ying Cui, Hui Liu, Giuseppe Caire
cs.IT math.IT