Device-to-Device (D2D) assisted coded caching is a promising approach to improve the communication efficiency over networks. However, the basic D2D coded caching scheme requires a subpacketization size that increases exponentially with the number of users. This is infeasible since the file size needs to be extremely large in the server. It is desirable to design a scheme that achieves a small subpacketization size while keeping the rate low. Recently, D2D placement delivery array (DPDA) was proposed to address the high subpacketization issue of D2D coded caching. This paper investigates the design of DPDA from the perspectives of linear algebraic and additive combinatorics. It is shown that a linear subspace possessing certain property can be employed in the design of DPDA. Based on this, a new D2D coded caching scheme with a subquadratic subpacketization size is derived through shortening the binary Reed-Muller codes. In order to obtain a D2D coded caching scheme with a linear subpacketization size, a new combinatorial structure called proper disjoint 3-term arithmetic progression (3-AP) free set is further introduced, and a deterministic algorithm for constructing it is provided with a polynomial complexity. Both the theoretical and numerical results reveal that the proposed schemes have a superior performance in terms of subpacketization size or transmission rate.

Coded caching is an effective technique to reduce the data transmission load by exploiting the cache contents across the network. However, most coded caching schemes are designed for static networks that consist of only a placement phase and a delivery phase. In practice, a network maybe dynamic with multiple rounds of placement and delivery phases, and the number of users within the network may vary. In these dynamic networks, a conventional coded caching scheme may lead to the undesired updates at the existing users’ cache contents. This paper proposes a centralized coded caching scheme for dynamic networks that can support multiple rounds with newly joining users. It prevents cache contents of the existing users from being updated, extending the service duration of cache devices. Further recognizing the need of information security in coded caching, the considered dynamic networks are featured by two constraints: 1) the library files must be kept secure from a wiretapper who has access to the shared link; 2) any subset of users cannot obtain information from the demands of other users. This consideration leads to another dynamic coded caching scheme that ensures information security. It is shown that the proposed schemes can yield a small subpacketization level and achieve a good rate-memory tradeoff.

Coded caching is an effective technique to reduce the data transmission load by exploiting the cache contents across the network. However, most coded caching schemes are designed for static networks that consist of only a placement phase and a delivery phase among a constant number of users. In practice, a network maybe dynamic with multiple rounds of placement and delivery phases, and the number of users may vary. In such dynamic networks, a conventional coded caching scheme may lead to the undesired content updates at the users’ cache, which is caused by the newly joining users. This paper proposes a centralized coded caching scheme for dynamic networks that can support multiple rounds and accommodate the newly joining users during this process. It prevents cache contents of the existing users from being updated. It is shown that the proposed scheme can yield a reduced subpacketization level and achieve a good rate-memory tradeoff.

Coded caching is an effective technique to decongest the amount of traffic in the backhaul link. In such a scheme, each file hosted in the server is divided into a number of packets to pursue a low broadcasting rate based on the designed placements at each user’s cache. However, the implementation complexity of this scheme increases with the number of packets. It is important to design a scheme with a small subpacketization level and a relatively low transmission rate. Recently, placement delivery array (PDA) was proposed to address the subpacketization bottleneck of coded caching. This paper investigates the design of PDA from a new perspective, i.e., the injective arc coloring of regular digraphs. It is shown that the injective arc coloring of a regular digraph can yield a PDA with the same number of rows and columns. Based on this, a new class of regular digraphs are defined and the upper bounds on the injective chromatic index of such digraphs are derived. Consequently, four new coded caching schemes with a linear subpacketization level and a relatively small transmission rate are proposed, one of which generalizes the existing scheme for the scenario with a more flexible number of users.

Coded caching is an effective technique to utilize multicasting opportunities to reduce the data transmission load in cached networks. In such a scheme, each file in the data center or library is usually divided into a number of packets to pursue a low broadcasting rate based on the designed placements at each user’s cache. However, the implementation complexity of this scheme increases with the number of packets. It is crucial to design a scheme with a small subpacketization level, while maintaining a relatively low transmission rate. Recently, a combinatorial structure called placement delivery array (PDA) was proposed as an effective tool to design coded caching schemes with a low subpacketization level. This paper proposes a novel PDA construction by selecting proper orthogonal arrays (POAs). It generalizes the existing construction, making it suitable to the scenario with a more flexible memory size. Based on the proposed PDA construction, a new coded caching scheme with the coded placement is further proposed. It is shown that the proposed schemes can yield a lower subpacketization level or transmission rate over the benchmark schemes.

Coded caching is an emerging technique to reduce the data transmission load during the peak-traffic times. In such a scheme, each file in the data center or library is divided into a number of packets to pursue a low broadcasting rate based on the designed placements at each user’s cache. However, the implementation complexity of this scheme increases with the number of packets. It is crucial to design a scheme with a small subpacketization level, while maintaining a relatively low transmission rate. Recently, a combinatorial structure called placement delivery array (PDA) was proposed as an effective tool to design coded caching schemes with a relatively low subpacketization level. This paper proposes a novel PDA construction by selecting proper orthogonal arrays (POAs), which generalizes the existing construction but with a more flexible memory size. Based on the proposed PDA construction, an effective transform is further proposed to enable a coded caching scheme to achieve a smaller subpacketization level. Moreover, two new coded caching schemes with the coded placement are derived. It is shown that the proposed schemes can yield a lower subpacketization level or transmission rate over the benchmark schemes.