Cache-Aided Scalar Linear Function Retrieval
Kai Wan, Hua Sun, Mingyue Ji, Daniela Tuninetti, Giuseppe Caire · 2020
In the shared-link coded caching problem, formulated by Maddah-Ali and Niesen (MAN), each cache-aided user demands one file (i.e., single file retrieval). This paper generalizes the MAN problem so as to allow users to request scalar linear functions (aka, linear combinations with scalar coefficients) of the files. We propose a novel coded delivery scheme, based on MAN uncoded cache placement, that allows for the decoding of arbitrary scalar linear functions of the files on arbitrary finite fields. Surprisingly, it is shown that the load for cache-aided scalar linear function retrieval depends on the number of linearly independent functions that are demanded, akin to the cache-aided single-file retrieval problem where the load depends on the number of distinct file requests. The proposed scheme is proved to be optimal under the constraint of uncoded cache placement, in terms of worst-case load, and within a factor 2 otherwise.