Coded caching has emerged as an effective technique to alleviate network congestion. While the individual impact of user cache sizes or file popularity has been investigated independently, their joint impact on coded caching remains unclear. In this paper, we first characterize two information-theoretic lower bounds on the expected transmission rate. The first bound introduces a novel cut-set method that allows users to repeatedly request files at different frequencies, accounting for the heterogeneity of user cache sizes and file popularity. The second bound is derived from the traditional cut-set bound, assuming each file is requested at most once. Then a group-based multi-round decentralized coded caching scheme is introduced. We show that the expected transmission rate for this scheme is at most anO(logK) factor away from the second lower bound, applicable to any cache and popularity distributions, whereKis the number of users. Additionally, by combining with the first lower bound, a tighterO(logKmK/m1) gap between the upper and lower bounds is derived for power function and Zipf cache distributions, wherem1andmKrepresent the minimum and maximum cache sizes, respectively. Simulation results show the superior performance of our proposed scheme.

Coded caching has emerged as a promising technique to alleviate traffic congestion by strategically creating coded multicasting opportunities, even for caches with different demands. For a two-layer cache-aided hierarchical network consisting of a central server, multiple helpers, and multiple users, prior works have characterized the fundamental performance limits of coded caching for this system with the constraint of a uniform user distribution (i.e., each helper serves an equal number of users). However, when the heterogeneity of user distribution is taken into account, there remain open questions. In this article, we consider a two-layer cache-aided hierarchical network with arbitrary user distributions, where a central server is connected via an error-free link to multiple helpers and each user can randomly access one helper. We introduce a new decentralized coded caching scheme and employ the cut-set technique to characterize lower bounds. Our results show that the gap between the upper and lower bound of the achievable rate from server to helpers is within a constant multiplicative (i.e., [1/32]) and additive (i.e., 2) factor, outperforming prior works under uniform user distribution. Moreover, we also show that the transmission rate from each helper to its attached users is at most a constant factor away from the corresponding lower bound. To our knowledge, this is the first work in hierarchical networks to eliminate the additive gap of the second layer. Finally, simulation results demonstrate the superiority of the proposed caching scheme compared with the state of the art.

Coded caching is an effective method to reduce the traffic load on network bottleneck. While the heterogeneities on the number of requests and cache sizes in coded caching have been studied independently, their joint impact is still unclear. This paper investigates coded caching in scenarios with heterogeneous number of requests and cache sizes. We propose two achievable schemes. The first scheme, based on file grouping and multi-round decentralized coded caching, is demonstrated to be order optimal under the worst setting, i.e., when user with the i-th smallest cache has the i-th largest number of requests. Moreover, we obtain an important insight that the lower bound of the achievable rate is predominantly influenced by users with high$\frac {X_{i}}{M_{i}}$ratios, where$X_{i}$and$M_{i}$represent the number of requests and cache size of user i, respectively. Since the achievable rate of our first scheme is difficult to analyze in the general setting, we further propose the second scheme to derive a tractable upper bound. Based on the insight, the second scheme rearranges the users according to their$\frac {X_{i}}{M_{i}}$ratios and employs a threshold to divide them into the head users who may have a large impact on the lower bound, and the tail users who may have a small impact on the lower bound. The server transmits the demands of the head users directly while applying the first scheme in groups among the tail users. Under the general setting, the gap between the rate of our second scheme and the lower bound is proved to be within a logarithmic factor. Simulations are conducted to verify the superior performance of our proposed schemes.

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 α not less than 1, we can obtain a constant gap, while when α is less then 1, the gap is bounded by 28 log N if $r \geq \frac{h}{{\log N}}$.