A New Order-Optimal Decentralized Coded Caching Scheme With Good Performance in the Finite File Size Regime

The decentralized coded caching scheme of Maddah-Ali and Niesen for the shared link network achieves an order-optimal memory-load tradeoff when the file size goes to infinity. It is then successively shown by Shanmugam et al. that, in the practical operating regime where the file size is finite, such a scheme yields a much less attractive coded caching gain. In this paper, we focus on designing decentralized coded caching schemes that can achieve low worst case loads of the shared link when the file size is finite and maintain order-optimal memory-load tradeoffs when the file size grows to infinity. First, we propose a decentralized coded caching design framework for designing decentralized coded caching schemes that can achieve significantly lower worst case loads than Maddah-Ali-Niesen's decentralized coded caching scheme in the finite file size regime while maintaining order-optimal memory-load tradeoffs when the file size grows to infinity. Then, within the proposed framework, we propose a decentralized coded caching scheme, which is simple and tractable, and can achieve a low worst case load in both the finite and infinite file size regimes. We analyze the worst case load of the proposed scheme and show that it outperforms Maddah-Ali-Niesen's and Shanmugam et al.'s decentralized schemes in the finite file size regime when the number of users is not too small. We also analyze the asymptotic worst case load of the proposed scheme when the file size goes to infinity and show that the proposed scheme achieves an order-optimal memory-load tradeoff. Finally, we analytically characterize the behavior of the worst case coded caching gain of the proposed scheme as a function of the required file size when the file size is large.