  Caching is a promising solution to satisfy the ongoing explosive demands for
multi-media traffics. Recently, Maddah-Ali and Niesen proposed both centralized
and de-centralized coded caching schemes, which are able to attain significant
performance gains over uncoded caching schemes. Particular, their work
indicates that there exists a performance gap between the decentralized coded
caching scheme and the centralized coded caching scheme. In this paper, we
investigate this gap. As a result, we 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. Notably, both bounds are achievable in some cases.
Furthermore, we prove that the gap can be arbitrarily close to 1 if the number
of users is large enough, which suggests the great potential in practical
applications to use the less optimal but more practical decentralized coded
caching scheme
