Capacity of 2-User Linear Computation Broadcast With Partially Informed Server

Abstract

A linear computation broadcast (LCBC) setting is comprised of data that is stored at a server and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> users who wish to retrieve their respective desired linear functions of the data, while utilizing knowledge of certain other linear functions available to each user as prior side-information. The goal is to determine the smallest amount of broadcast information from the server that will simultaneously satisfy all the users’ demands. The reciprocal of the optimal broadcast cost is called the capacity of LCBC. The capacity is known for the 2-user setting, and recent studies of 3-user LCBC have revealed new insights into the need for sumset inequalities for LCBC. This letter introduces a generalization of the LCBC problem, where instead of storing all the data, the server may have partial knowledge in the form of some arbitrary linear function of the data. Building upon recent advances, the exact capacity is found for 2-user linear computation broadcast with partially informed server.