Coded Caching in Combination Networks with Heterogeneous Caches

Coded caching technique is an effective method to reduce peak traffic. We consider coded caching in combination networks in which a server with a library of N files connects to users through h relay nodes and each user with cache connects to different sets of r relay nodes. Previous works are always assumed that the users' cache capacity is consistent, but this is quite different from the actual application scenarios. The cache capacity of users connected to the network may vary widely. In this paper, we investigate combination networks with heterogeneous caches. For this setting, we propose a decentralized coded caching scheme for any combination network and derive the upper bound of transmission rate. Then, we derive the lower bound for any transmission scheme. We also analyze the gap between upper and lower bounds under the case that the user cache sizes follow Zipf distributions. For Zipf distributions with a not less than 1, we can obtain a constant gap, while when a is less then 1, the gap is bounded by 28 logN if r >= h/log N.