On the Placement Delivery Array Design in Centralized Coded Caching Scheme

TL;DR

This paper introduces a novel placement delivery array (PDA) design framework for centralized coded caching, reducing the file splitting complexity while maintaining high coding gains, thus enhancing practical caching system implementations.

Contribution

It formulates the PDA design problem, shows the connection to existing schemes, and proposes new PDA constructions that significantly reduce file splitting requirements.

Findings

Ali-Niesen scheme is a special PDA with optimal coding gain.

New PDA constructions decrease the number of file packets from exponential order.

The new schemes maintain near-optimal coding gain with reduced complexity.

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 $q\geq 2$). The new construction can decrease the required $F$ from the order $O\left(e^{K\cdot\left(\frac{M}{N}\ln \frac{N}{M} +(1-\frac{M}{N})\ln \frac{N}{N-M}\right)}\right)$ of Ali-Niesen scheme to $O\left(e^{K\cdot\frac{M}{N}\ln \frac{N}{M}}\right)$ or $O\left(e^{K\cdot(1-\frac{M}{N})\ln\frac{N}{N-M}}\right)$ respectively, while the coding gain loss is only $1$.