Multi-user linearly separable computation

In this work, we investigate the problem of multi-user linearly separable computation, where N servers help compute the desired functions of K users while each desired function can be written as a linear combination of up to L (generally non-linear) sub-functions. Each server computes some of the subtasks, and communicates a linear combination of its computed outputs (files) in a single-shot to some of the users, where each user then linearly combines its received data in order to recover its desired function. We explore the range of the optimal computation cost via establishing a novel relationship with coding theory.