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Register a new userSecretive Coded Caching from PDAs
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Added by
B.Sundar Rajan
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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The coded caching problem with secrecy constraint i.e., the users should not be able to gain any information about the content of the files that they did not demand, is known as the secretive coded caching problem. This was proposed by Ravindrakumar et al. in the paper titled ``Private Coded Caching that appeared in emph{ IEEE Transactions on Information Forensics and Security}, 2018 and is characterised by subpacketization levels growing exponentially with the number of users. In the context of coded caching without secrecy, coded caching schemes at subexponential subpacketization levels are feasible by representing the caching system in the form of a Placement Delivery Array (PDA) and designing placement and delivery policies from it. Motivated by this, we propose a secretive coded caching scheme with low subpacketization using PDA, for users with dedicated caches in the centralized setting. When our scheme is applied to a special class of PDA known as MN PDA, the scheme proposed by Ravindrakumar et al. is recovered.
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We consider the problem of emph{secretive coded caching} in a shared cache setup where the number of users accessing a particular emph{helper cache} is more than one, and every user can access exactly one helper cache. In secretive coded caching, the constraint of emph{perfect secrecy} must be satisfied. It requires that the users should not gain, either from their caches or from the transmissions, any information about the content of the files that they did not request from the server. In order to accommodate the secrecy constraint, our problem setup requires, in addition to a helper cache, a dedicated emph{user cache} of minimum capacity of 1 unit to every user. This is where our formulation differs from the original work on shared caches (``Fundamental Limits of Coded Caching With Multiple Antennas, Shared Caches and Uncoded Prefetching by E.~Parrinello, A.~{{U}}nsal and P.~Elia in Trans. Inf. Theory, 2020). In this work, we propose a secretively achievable coded caching scheme with shared caches under centralized placement. When our scheme is applied to the dedicated cache setting, it matches the scheme by Ravindrakumar emph{et al.} (``Private Coded Caching, in Trans. Inf. Forensics and Security, 2018).
We consider multi-access coded caching problem introduced by Hachem et.al., where each user has access to $L$ neighboring caches in a cyclic wrap-around fashion. We focus on the deterministic schemes for a specific class of multi-access coded caching problem based on the concept of PDA. We construct new PDAs which specify the delivery scheme for the specific class of multi-access coded caching problem discussed in this paper. For the proposed scheme, the coding gain is larger than that of the state-of-the-art while the sub-packetization level varies only linearly with the number of users. Hence, we achieve a lower transmission rate with the least sub-packetization level compared to the existing schemes.
Coded caching schemes with low subpacketization and small transmission rate are desirable in practice due to the requirement of low implementation complexity and efficiency of the transmission. Placement delivery arrays (PDA in short) can be used to generate coded caching schemes. However, many known coded caching schemes have large memory ratios. In this paper, we realize that some schemes with low subpacketization generated by PDAs do not fully use the users caching content to create multicasting opportunities and thus propose to overcome this drawback. As an application, we obtain two new schemes with low subpacketizations, which have significantly advantages on the memory ratio and transmission rate compared with the original scheme.
In this paper, we consider the coded-caching broadcast network with user cooperation, where a server connects with multiple users and the users can cooperate with each other through a cooperation network. We propose a centralized coded caching scheme based on a new deterministic placement strategy and a parallel delivery strategy. It is shown that the new scheme optimally allocate the communication loads on the server and users, obtaining cooperation gain and parallel gain that greatly reduces the transmission delay. Furthermore, we show that the number of users who parallelly send information should decrease when the users caching size increases. In other words, letting more users parallelly send information could be harmful. Finally, we derive a constant multiplicative gap between the lower bound and upper bound on the transmission delay, which proves that our scheme is order optimal.
In coded caching system we prefer to design a coded caching scheme with low subpacketization and small transmission rate (i.e., the low implementation complexity and the efficient transmission during the peak traffic times). Placement delivery arrays (PDA) can be used to design code caching schemes. In this paper we propose a framework of constructing PDAs via Hamming distance. As an application, two classes of coded caching schemes with linear subpacketizations and small transmission rates are obtained.
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