Cache Placement Optimization for Coded Caching with Arbitrary Cache Size
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We consider content caching between a service provider and multiple cache-enabled users, using the recently proposed modified coded caching scheme (MCCS) with an improved delivery strategy. We develop the optimal cache placement scheme through formulating a cache placement optimization problem, aiming to minimize the average load during the delivery phase under arbitrary cache size and user requests. Through reformulation, we show that the problem is a linear programming problem. By exploring the properties in the caching constraints, we derive the optimal cache placement solution in closed-form, offering the complete optimal cache placement solution for any cache size and user population. We verify that the existing optimal scheme obtained at specific cache sizes is a special case of our solution. Through numerical studies, we show an interesting pattern of the optimal cache placement as the cache size varies, as well as the pattern of caching gain under the optimal caching as the number of users varies.
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