[Paper Review] Fundamental Structure of Optimal Cache Placement for Coded Caching with Heterogeneous Demands

Yong Deng, Min Dong|arXiv (Cornell University)|Dec 2, 2019

Caching and Content Delivery4 citations

TL;DR

This paper characterizes the optimal uncoded cache placement for coded caching with heterogeneous demands under nonuniform file popularity, proving that at most three file groups exist in the optimal solution. It derives closed-form solutions for each grouping case and proposes a simple algorithm to compute the optimal placement, revealing that coding across file groups during delivery can be beneficial and tightening the information-theoretic converse bound while showing subpacketization scales as $\mathcal{O}(2^K/\sqrt{K})$ for $K$ users.

ABSTRACT

This paper studies the caching system of multiple cache-enabled users with heterogeneous demands. Under nonuniform file popularity, we thoroughly characterize the structure of the optimal uncoded cache placement for the coded caching scheme (CCS). Formulating the cache placement as an optimization problem to minimize the average delivery rate, we identify the file grouping structure under the optimal solution. We show that, regardless of file popularity, there are at most three file groups under the optimal cache placement. We further characterize the complete structure of the optimal cache placement and obtain the closed-form solution in each possible file grouping case. A simple algorithm is developed to obtain the final optimal cache placement, which only computes a set of candidate closed-form solutions in parallel. We provide insights into the file groups formed by the optimal cache placement. The optimal placement solution also indicates that coding between file groups may be explored during delivery, in contrast to the existing heuristic file grouping schemes. Using the file grouping in the optimal cache placement, we propose a new information-theoretic converse bound for coded caching that is tighter than existing ones. Moreover, using the optimal cache placement solution, we characterize the file subpacketization in the optimal CCS and show that the maximum subpacketization level in the worst case scales as $\mathcal{O}(2^K/\sqrt{K})$ for $K$ users.

Motivation & Objective

• To determine the optimal uncoded cache placement strategy in coded caching systems with heterogeneous user demands and nonuniform file popularity.
• To identify the structural properties of the optimal cache placement that minimize the average delivery rate.
• To develop a simple algorithm that computes the optimal placement by evaluating a small set of candidate closed-form solutions.
• To provide new insights into file grouping and the potential for inter-group coding during delivery.
• To derive a tighter information-theoretic converse bound and characterize the maximum subpacketization level in the optimal coded caching scheme.

Proposed method

• Formulates the cache placement as a rate minimization optimization problem under nonuniform file popularity.
• Identifies that the optimal solution partitions files into at most three distinct groups based on popularity and demand patterns.
• Derives closed-form expressions for the optimal cache placement for each possible file grouping configuration.
• Proposes a practical algorithm that evaluates candidate solutions in parallel to efficiently determine the global optimum.
• Uses the optimal file grouping structure to construct a new information-theoretic converse bound, improving upon existing bounds.
• Analyzes the worst-case subpacketization level and proves it scales as $\mathcal{O}(2^K/\sqrt{K})$ for $K$ users.

Experimental results

Research questions

• RQ1 What is the maximum number of file groups that can exist in the optimal uncoded cache placement for coded caching with heterogeneous demands?
• RQ2 How does file popularity influence the structure of the optimal cache placement?
• RQ3 Can coding across different file groups during delivery improve system performance, and if so, under what conditions?
• RQ4 What is the tightest possible information-theoretic converse bound for coded caching under nonuniform file popularity?
• RQ5 How does the maximum subpacketization level scale with the number of users in the optimal coded caching scheme?

Key findings

• The optimal cache placement partitions files into at most three groups, regardless of file popularity distribution.
• A simple algorithm exists that computes the optimal placement by evaluating only a small set of candidate closed-form solutions in parallel.
• The optimal file grouping structure enables inter-group coding during delivery, challenging the assumption of intra-group coding only in prior heuristic schemes.
• A new information-theoretic converse bound is derived that is tighter than existing bounds, leveraging the optimal file grouping.
• The maximum subpacketization level in the worst case scales as $\mathcal{O}(2^K/\sqrt{K})$ for $K$ users, which is a significant characterization of system complexity.