An Improved Multi-access Coded Caching with Uncoded Placement

Abstract

In this work, we consider a slight variant of well known coded caching problem, referred as multi-access coded caching problem, where each user has access to z neighboring caches in a cyclic wrap-around way. We present a placement and delivery scheme for this problem, under the restriction of uncoded placement. Our work is a generalization of one of the cases considered in "Multi-access coded caching : gains beyond cache-redundancy" by B. Serbetci, E. Parrinello and P. Elia. To be precise, when our scheme is specialized to z = K−1 Kγ , for any Kγ, where K is the number of users and γ is the normalized cache size, we show that our result coincides with their result. We show that for the cases considered in this work, our scheme outperforms the scheme proposed in "Rate-memory trade-off for multi-access coded caching with uncoded placement" by K. S. Reddy and N. Karamchandani, except for some special cases considered in that paper. We also show that for z = K − 1, our scheme achieves the optimal transmission rate.

Multiaccess Coded Caching with Private Demands

“…By comparing the requirements in Theorem 1 and the existing non-private multiaccess coded caching schemes in [12], [13], [15], [16], [18], [17] ( reviewed in Section II-B), it can be seen that all of those schemes satisfy Requirements 1,2,3 in Theorem 1. For simplicity, here we only take the two results in [13] as examples and obtain the following theorems.…”

“…As the applications, two new multiaccess coded caching schemes were obtained based on the MN scheme and partition scheme in [14]. It is worth noting that the first scheme in [13] achieves the transmission load K(1−LM/N ) KM/N +1 for any positive integers L and K. In [15], [16], [17], [18], other constructions of multiaccess coded caching schemes were proposed based on uncoded cache placement (i.e., each cache-node only cache subset of library bits) and linear delivery coding scheme.…”

“…In addition, it derived a lower bound under the restriction of uncoded cache placement and L ≥ K 2 , and shown that the multiplicative gap between the new achievable rate and the lower bound is at most 2. Then the authors in [16] proposed a multiaccess coded caching scheme, whose achievable load is better than the achievable load in [15].…”

Multi-Access Cache-Aided Multi-User Private Information Retrieval

“…-In Theorem 2 we show that the rate achieved in Theorem 1 is order optimal within a multiplicative factor of 2 assuming uncoded storage. -In Theorem 3 we give an achievable rate for the special case of cyclic wraparound cache access systems widely studied [11], [12], [13], [14], [15], [16]. The achievable scheme is given in Section V.…”

“…This cyclic wraparound coded caching has been widely studied [11], [12], [13], [14], [15], [16]. Before stating the rate for this setup, for integers m ≤ k < n, we define cyc(n, k, m) to be the number of k sized subsets of n distinguishable elements arranged in a circle, such that there is atleast one set of m consecutive elements amongst those k elements.…”