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Each video clip has different degrees of popularity and a user can cache some popular videos in preparation for future requests. The cached data work as a buffer against the playback delay due to unstable wireless channels. Since the storage space for caching is limited while the number of video clips is tremendously large, a memory efficient caching strategy is important for maximizing the caching gain. We propose a user prefix caching scheme in a downlink network where each user caches an initial part (i.e., prefix) of each popular video to minimize the average playback delay. We derive closed-form expressions of the optimal prefix size and the corresponding average playback delay. Our results show the effects of system parameters on the average playback delay and provide an insightful guideline on memory-efficient caching. Moreover, in the scenarios where a constraint on tolerable delay is given, we …