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Register a new userNew coded caching schemes from placement delivery arrays
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Minquan Cheng
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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.
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In caching system, it is desirable to design a coded caching scheme with the transmission load $R$ and subpacketization $F$ as small as possible, in order to improve efficiency of transmission in the peak traffic times and to decrease implementation complexity. Yan et al. reformulated the centralized coded caching scheme as designing a corresponding $Ftimes K$ array called placement delivery array (PDA), where $F$ is the subpacketization and $K$ is the number of users. Motivated by several constructions of PDAs, we introduce a framework for constructing PDAs, where each row is indexed by a row vector of some matrix called row index matrix and each columns index is labelled by an element of a direct product set. Using this framework, a new scheme is obtained, which can be regarded as a generalization of some previously known schemes. When $K$ is equal to ${mchoose t}q^t$ for positive integers $m$, $t$ with $t<m$ and $qgeq 2$, we show that the row index matrix must be an orthogonal array if all the users have the same memory size. Furthermore, the row index matrix must be a covering array if the coded gain is ${mchoose t}$, which is the maximal coded gain under our framework. Consequently the lower bounds on the transmission load and subpacketization of the schemes are derived under our framework. Finally, using orthogonal arrays as the row index matrix, we obtain two more explicit classes of schemes which have significantly advantages on the subpacketization while the transmission load is equal or close to that of the schemes constructed by Shangguan et al. (IEEE Trans. Inf. Theory, 64, 5755-5766, 2018) for the same number of users and memory size.
The multi-access variant of the coded caching problem in the presence of an external wiretapper is investigated . A multi-access coded caching scheme with $K$ users, $K$ caches and $N$ files, where each user has access to $L$ neighbouring caches in a cyclic wrap-around manner, is proposed, which is secure against the wiretappers. Each transmission in the conventional insecure scheme will be now encrypted by a random key. The proposed scheme uses a novel technique for the key placement in the caches. It is also shown that the proposed secure multi-access coded caching scheme is within a constant multiplicative factor from the information-theoretic optimal rate for $Lgeq frac{K}{2}$ and $Ngeq 2K$.
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.
Recently multi-access coded caching schemes with number of users different from the number of caches obtained from a special case of resolvable designs called Cross Resolvable Designs (CRDs) have been reported and a new performance metric called rate-per-user has been introduced cite{KNRarXiv}. In this paper we present a generalization of this work resulting in multi-access coded caching schemes with improved rate-per-user.
In an $(H,r)$ combination network, a single content library is delivered to ${Hchoose r}$ users through deployed $H$ relays without cache memories, such that each user with local cache memories is simultaneously served by a different subset of $r$ relays on orthogonal non-interfering and error-free channels. The combinatorial placement delivery array (CPDA in short) can be used to realize a coded caching scheme for combination networks. In this paper, a new algorithm realizing a coded caching scheme for combination network based on a CPDA is proposed such that the schemes obtained have smaller subpacketization levels or are implemented more flexible than the previously known schemes. Then we focus on directly constructing CPDAs for any positive integers $H$ and $r$ with $r<H$. This is different from the grouping method in reference (IEEE ISIT, 17-22, 2018) under the constraint that $r$ divides $H$. Consequently two classes of CPDAs are obtained. Finally comparing to the schemes and the method proposed by Yan et al., (IEEE ISIT, 17-22, 2018) the schemes realized by our CPDAs have significantly advantages on the subpacketization levels and the transmission rates.
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