  This paper analyzes the achievable tradeoff between cache~size and
download~rate in decentralized caching systems with the uncoded cache placement
originally proposed by Maddah-Ali and Niesen. It proposes two novel delivery
schemes that take advantage of the multicasting opportunities that arise when a
file is demanded by multiple users. These delivery schemes are extensions of
known ones to the regime where the file size is finite. Numerical evaluations
for the case of file uniform popularity show that the proposed schemes
outperform previous ones for all value of the cache size.
