On the Placement Delivery Array Design for Centralized Coded Caching Scheme

Abstract

Caching is a promising solution to satisfy the ever increasing demands for the multi-media traffics. In caching networks, coded caching is a recently proposed technique that achieves significant performance gains over the uncoded caching schemes. However, to implement the coded caching schemes, each file has to be split into F packets, which usually increases exponentially with the number of users K. Thus, designing caching schemes that decrease the order of F is meaningful for practical implementations. In this paper, by reviewing the Ali-Niesen caching scheme, the placement delivery array (PDA) design problem is firstly formulated to characterize the placement issue and the delivery issue with a single array. Moreover, we show that, through designing appropriate PDA, new centralized coded caching schemes can be discovered. Secondly, it is shown that the Ali-Niesen scheme corresponds to a special class of PDA, which realizes the best coding gain with the least F . Thirdly, we present a new construction of PDA for the centralized caching system, wherein the cache size of each user M (identical cache size is assumed at all users) and the number of files N satisfies M/N = 1/q or (q − 1)/q (q is an integer such that q ≥ 2). The new construction can decrease the required F from the order O e

A New Capacity-Achieving Private Information Retrieval Scheme With (Almost) Optimal File Length for Coded Servers

“…Although large file length can contribute to improve retrieval rate, it also arouses complexity increase in practical implementations. The problem of decreasing the file length, also known as subpacketization in the literature, has been noted in many applications, for example coded caching [9,14,15], while it becomes the bottleneck for practical application of the PIR scheme in [10]. The file length of capacity-achieving PIR schemes was reduced to N M−1 in [11] subsequently.…”

Content Caching and Delivery in Wireless Radio Access Networks

“…First, given the overhead and feasibility of estimating the global channel state information (CSI), it is of great importance to analyze the caching gain in the presence of imperfect or delayed channel state information. Second, most current caching schemes as well as those considered in this paper still suffer from the exponential sub-packetization problem, which would impede practical implementation when the numbers of ENs and UEs become large [45]; therefore, low sub-packetization for cache placement is an important research direction [46]. Third, while the new contributions in this paper and a majority of the existing works in the literature focus on the asymptotic NDT analysis, as it lends itself to closed-form expressions, whose order optimality can be proven in certain cases, both finite SNR analysis and finite block-length analysis are also important to validate the conclusions reached through NDT analysis.…”

Placement Delivery Arrays from Combinations of Strong Edge Colorings

“…Let W = {W 1 , ..., W N } be the set of files, K = {1, ..., K} denote the K users, and F = {1, ..., F } be a set of cardinality F . Yan et al, in [11], proposed the PDA as a method for designing a (K, M, N ) coded caching scheme that can be expressed in a single array. A PDA is an array P = [p j,k ] F ×K of size F × K, where both F and F M/N are integers.…”

“…For some good examples of PDAs where the decoding process is shown in detail, the reader is referred to [9], [11] and [12].…”

“…Yan et al, in [11], represent the coded caching scheme by a single array which they call a placement delivery array (PDA). In short, a PDA can be thought of as having two phases.…”