Coded Caching for Heterogeneous Systems: An Optimization Perspective

TL;DR

This paper investigates the fundamental trade-offs in coded caching for heterogeneous systems, optimizing cache placement and delivery strategies to minimize server load and delivery time under various constraints.

Contribution

It introduces optimized uncoded placement and linear delivery schemes for heterogeneous cache sizes, deriving bounds and characterizations for different system configurations.

Findings

Explicit characterization of the cache-memory trade-off for three users.

Optimal cache size allocation minimizes delivery time considering link capacities.

Derived lower bounds for uncoded placement in heterogeneous settings.

Abstract

In cache-aided networks, the server populates the cache memories at the users during low-traffic periods, in order to reduce the delivery load during peak-traffic hours. In turn, there exists a fundamental trade-off between the delivery load on the server and the cache sizes at the users. In this paper, we study this trade-off in a multicast network where the server is connected to users with unequal cache sizes and the number of users is less than or equal to the number of library files. We propose centralized uncoded placement and linear delivery schemes which are optimized by solving a linear program. Additionally, we derive a lower bound on the delivery memory trade-off with uncoded placement that accounts for the heterogeneity in cache sizes. We explicitly characterize this trade-off for the case of three end-users, as well as an arbitrary number of end-users when the total memory size at the users is small, and when it is large. Next, we consider a system where the server is connected to the users via rate limited links of different capacities and the server assigns the users' cache sizes subject to a total cache budget. We characterize the optimal cache sizes that minimize the delivery completion time with uncoded placement and linear delivery. In particular, the optimal memory allocation balances between assigning larger cache sizes to users with low capacity links and uniform memory allocation.