  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.
