The model considered in this work consists ofHservers where the file library is Maximum Distance Separable (MDS) coded and stored. Each server is connected toKusers through a dedicated shared link, and each user has access to a unique set ofrout ofCcaches. For every set ofrcaches, there is a user. Each user aims to retrieve an arbitrary linear combination of files. All the users should be able to retrieve their demands using the signals from anyLout ofHservers. In addition, the following conditions must be satisfied: (a) content-security from an eavesdropper, b) demand-privacy against non-colluding users and any colluding set of servers. We propose two schemes, one of which satisfies both the above conditions and the other satisfies only the security condition. Over a certain range in the low memory region, our schemes are within a constant multiplicative factor from the optimal. As special cases, our schemes recover some of the previous works in the literature. One of our schemes is extended to a more general setup where different users are connected to different numbers of caches, and multiple users are connected to the same subset of caches.

In this work, we consider the multi-access combinatorial topology with C caches where each user accesses a unique set of r caches. For this setup, we consider secrecy, where each user should not know anything about the files it did not request, and demand privacy, where each user’s demand must be kept private from other non-colluding users. We propose a scheme satisfying both conditions and derive a lower bound based on cut-set arguments. Also, we prove that our scheme is optimal when r ≥ C − 1, and it is order-optimal when the cache memory size M is greater than or equal to a certain threshold for r < C − 1. When r = 1, in most of the memory region, our scheme achieves the same rate as the one given by the secretive scheme for the dedicated cache setup by Ravindrakumar et al. (’Private Coded Caching,’ in IEEE Transactions on Information Forensics and Security, 2018), while satisfying both secrecy and demand privacy conditions.

In this work, the problem setup consists of a server with$N$files connected to$K$users through an error-free shared link. Also, it consists of$C$caches of size$M_{M}\mathbf{files}$called multi-access caches and$K$caches of size$M_{P}$files called private caches. Each user is connected to a private cache and to a unique set of$r$multi-access caches. For every set of$r$multi-access caches, there is a user. For this setup a scheme is proposed that satisfies the following simultaneously: a) Linear Function Retrieval (LFR), b) content-security from an eavesdropper, and c) demand-privacy against a colluding set of users. It is shown that the private caches included in this work, enables the proposed scheme to provide privacy against colliding users. Also it is shown that to achieve the same rate both in [17] and in the proposed scheme, the total memory accessed by each user is less in the proposed scheme. Moreover, it turns out that the total cache memory requirement is also less for the system considered in this work compared to that in [17]. When$r=1$, the proposed scheme recovers one of the schemes given by Yan and Tuninetti (“Key Superposition Simultaneously Achieves Security and Privacy in Cache-Aided Linear Function Retrieval,” in Trans. Inf. Forensics and Security, 2021).

In the original coded caching model introduced by Maddah-Ali and Niesen in 2014, the server starts broadcasting only after it receives demands from all the users. So, all the users must be active during the delivery phase. In this work, we consider a coded caching model called hotplug coded caching in which some of the users are offline during the delivery phase. This model was first introduced by Ma and Tuninetti (“On Coded Caching Systems with Offline Users,” 2022 IEEE International Symposium on Information Theory). The concept of Hotplug Placement Delivery Arrays (HpPDAs) for the hotplug coded caching systems was introduced in (“Improved Hotplug Caching Schemes Using PDAs and t-Designs,” arXiv:2311.02856, 2024), in which the authors have constructed HpPDAs from t-designs. This work provides a new hotplug coded caching scheme from the existing HpPDAs. The performance comparison of the proposed scheme with the existing schemes is presented. When applied for HpPDAs from t-designs, our scheme outperforms the baseline scheme by Ma and Tuninetti, and the Improved t-scheme by Rajput and Rajan in some memory segments.

A multi-access network consisting of C caches, K users with each user having access to unique set of r caches has been introduced recently. It considers Single File Retrieval (SFR) i.e, each user demands an arbitrary file from the server. It proposes a coded caching scheme which was shown to be optimal under the assumption of uncoded placement by Brunero and Elia ("Fundamental Limits of Combinatorial Multi-Access Caching" in arXiv:2110.07426 ). The above multi-access network is referred to as combinatorial topology which was considered in our work by imposing three additional constraints : a) Linear Function Retrieval (LFR) i.e., each user is interested in retrieving an arbitrary linear combination of the files in the server’s library; b) Security i.e., the content of the library must be kept secure from an eavesdropper who obtains the signal sent by the server; c) Privacy i.e., each user can only get its required file and can not get any information about the demands of other users. An achievable Secure, Private LFR (SP-LFR) scheme from which Private LFR (P-LFR), LFR schemes can be derived was proposed and also an achievable Secure LFR (S-LFR) scheme was proposed. In the higher memory region, rate achieved by SP-LFR scheme and P-LFR scheme will be same. When the access ratio (number of caches each user having access to) is 1, our SP-LFR scheme and P-LFR scheme reduces to MAN-PDA based SP-LFR scheme and MAN-PDA based P-LFR scheme respectively by Yan and Tuninetti ("Key Superposition Simultaneously Achieves Security and Privacy in Cache-Aided Linear Function Retrieval", in Trans. Inf. Forensics and Security, 2021) and our SP-LFR scheme, S-LFR and security key scheme for SFR by Sengupta et al. ("Fundamental limits of caching with secure delivery", in Trans. Inf. Forensics and Security, 2015 ) will have same performance.