On the Optimal Memory-Load Tradeoff of Coded Caching for Location-Based Content

Abstract

Caching at the wireless edge nodes is a promising way to boost the spatial and spectral efficiency, for the sake of alleviating networks from content-related traffic. Coded caching originally introduced by Maddah-Ali and Niesen significantly speeds up communication efficiency by transmitting multicast messages simultaneously useful to multiple users. Most prior works on coded caching are based on the assumption that each user may request all content in the library. However, in many applications the users are interested only in a limited set of content that depends on their location. For example, assisted self-driving vehicles may access super High-Definition maps of the area through which they are travelling. Motivated by these considerations, this paper formulates the coded caching problem for location-based content with edge cache nodes. The considered problem includes a content server with access to <inline-formula> <tex-math notation="LaTeX">${\mathsf N}$ </tex-math></inline-formula> location-based files (e.g., High-Definition maps), <inline-formula> <tex-math notation="LaTeX">${\mathsf K}$ </tex-math></inline-formula> edge cache nodes located at different regions, and <inline-formula> <tex-math notation="LaTeX">${\mathsf K}$ </tex-math></inline-formula> users (i.e., vehicles) each of which is in the serving region of one cache node and can retrieve the cached content of this cache node with negligible cost. Depending on the location, each user only requests a file from a location-dependent subset of the library. The objective is to minimize the worst-case load (i.e., the worst-case number of broadcasted bits from the content server among all possible demands). For this novel coded caching problem, we propose a highly non-trivial converse bound under uncoded cache placement (i.e., each cache node directly copies some library bits in its cache), which shows that a simple achievable scheme is optimal under uncoded cache placement. In addition, this achievable scheme is also proved to be generally order optimal within a factor of 3. Finally, we extend the coded caching problem for location-based content to the multiaccess coded caching topology originally proposed by Hachem <i>et al.</i>, where each user is connected to <inline-formula> <tex-math notation="LaTeX">${\mathsf L}$ </tex-math></inline-formula> nearest cache nodes. When <inline-formula> <tex-math notation="LaTeX">${\mathsf L}\geq 2$ </tex-math></inline-formula>, we characterize the exact optimality on the worst-case load.