On the Gap Between Decentralized and Centralized Coded Caching Schemes

Caching is a promising solution to satisfy the ongoing explosive demands for multi-media traffics. Recently, Maddah-Ali and Niesen proposed both centralized and decentralized coded caching schemes, which is able to attain significant performance gains over the uncoded caching schemes. Their work indicates that there exists performance gap between the decentralized coded caching scheme and the centralized coded caching scheme. In this paper, we focus on the gap between the performances of the decentralized and centralized coded caching schemes. Most notably, we strictly prove that the multiplicative gap (i.e., the ratio of their performances) is between 1 and 1.5. The upper bound tightens the original one of 12 by Maddah Ali and Niesen, while the lower bound verifies the intuition that the centralized coded caching scheme always outperforms its decentralized counterpart. In particular, both the two bounds are achievable in some cases. Furthermore, we prove that the gap can be arbitrarily close to 1 if the number of the users is large enough, which suggests the great potential in practical applications to use the less optimal but more practical decentralized coded caching scheme.