[Paper Review] Fundamental Rate-Memory Tradeoff for Coded Caching in Presence of User Inactivity

Jialing Liao, Olav Tirkkonen|arXiv (Cornell University)|Sep 29, 2021

Caching and Content Delivery37 references4 citations

TL;DR

This paper establishes the fundamental rate-memory tradeoff in coded caching under user inactivity, proposing a deterministic coded caching scheme that optimizes file subpacketization using fixed-cardinality fragment labeling. It proves that optimizing for user inactivity affects only delivery load, not cache placement, and shows centralized schemes closely match ideal performance with full inactivity knowledge, while decentralized schemes are slightly less robust under inactivity uncertainty.

ABSTRACT

Coded caching utilizes proper file subpacketization and coded delivery to make full use of the multicast opportunities in content delivery, to alleviate file transfer load in massive content delivery scenarios. Most existing work considers deterministic environments. An important practical topic is to characterize the impact of the uncertainty from user inactivity on coded caching. We consider a one server cache-enabled network under homogeneous file and network settings in presence of user inactivity. Unlike random or probabilistic caching studied in the literature, deterministic coded caching is considered, with the objective to minimize the worst-case backhaul load by optimizing the file subpacketization and the caching strategy. First, a coded caching method is used, where each file is split into the same type of fragments labeled using sets with fixed cardinality, and the optimality of the selected cardinality is proved. Optimal file subpacketization by splitting the file into multiple types of fragments labeled with multiple cardinalities is then discussed. We show that the closed-form optimum turns out to be given by a fixed cardinality -- optimizing for user inactivity only affects file delivery, cache placement is not affected. A decentralized version is also discussed and analyzed, where each user fills its storage independently at random without centralized coordination, and user inactivity is taken into account in file delivery. Simulation results show that the optimization based centralized coded caching scheme provides performance comparable to the ideal scenario assuming full knowledge of user inactivity in the placement phase, while decentralized caching performs slightly worse against user inactivity.

Motivation & Objective

• To characterize the impact of user inactivity on coded caching performance in a deterministic setting.
• To minimize worst-case backhaul load by optimizing file subpacketization and caching strategy under user inactivity.
• To prove that optimal file subpacketization uses a fixed cardinality for fragment labeling, independent of inactivity effects.
• To analyze both centralized and decentralized coded caching schemes under user inactivity, focusing on delivery load optimization.
• To compare performance of optimized centralized schemes with ideal scenarios assuming full inactivity knowledge during placement.

Proposed method

• Uses deterministic coded caching with file subpacketization via sets of fixed cardinality to label fragments.
• Proves optimality of fixed-cardinality labeling by analyzing the worst-case backhaul load via linear programming.
• Derives the rate-memory tradeoff by modeling delivery load as a function of user activity and subpacketization.
• Analyzes decentralized caching where users independently fill caches without coordination, adjusting delivery for inactivity.
• Compares centralized and decentralized schemes using simulation, evaluating performance against an ideal benchmark with full inactivity knowledge.
• Employs quadratic analysis and recursive comparison of load functions to determine sign behavior of performance differences.

Experimental results

Research questions

• RQ1 What is the optimal file subpacketization strategy in coded caching when user inactivity introduces uncertainty?
• RQ2 How does user inactivity affect the worst-case backhaul load in deterministic coded caching?
• RQ3 Does optimizing for user inactivity impact cache placement or only delivery?
• RQ4 How does the performance of a centralized coded caching scheme compare to an ideal scheme with full inactivity knowledge during placement?
• RQ5 How does decentralized coded caching perform under user inactivity compared to centralized schemes?

Key findings

• Optimal file subpacketization uses a fixed cardinality for fragment labeling, and this choice is independent of user inactivity.
• User inactivity affects only the delivery phase; cache placement remains unaffected by inactivity optimization.
• The centralized coded caching scheme achieves performance nearly identical to the ideal scenario with full inactivity knowledge during placement.
• The decentralized scheme performs slightly worse than the centralized scheme under inactivity, but remains robust.
• For K ≥ 9, the performance gain of the centralized scheme over decentralized increases with network size, as shown by the sign of ΔG(t+1) turning positive.
• The analysis proves that ΔG(t+1) > 0 for t ∈ [⌈K/2⌉−2, K−2] when K > 9, indicating consistent performance advantage of the centralized approach.