An Achievable Scheme for the K-user Linear Computation Broadcast Channel

TL;DR

This paper introduces a new scheme for the K-user Linear Computation Broadcast Channel that optimizes multicast messaging using subspace decomposition, extending previous results to arbitrary user numbers.

Contribution

It proposes a linear programming framework based on polymatroid spaces for designing multicast messages in K-LCBC, generalizing prior 3-user results.

Findings

Effective multicast message design for multiple users

Extension of 3-user results to arbitrary K

Framework applicable to linear coded caching problems

Abstract

This paper presents a new achievable scheme for the K-user Linear Computation Broadcast Channel (K-LCBC). A K-LCBC comprises data stored on a server and K users, each aiming to retrieve a desired linear function of the data by leveraging their prior locally available side information in the form of another linear function of the data. The proposed scheme is based on a subspace decomposition derived from representable polymatroid spaces. This decomposition enables the server to effectively design multicast messages that simultaneously benefit multiple users and allow users to eliminate interference using their available side information. This work extends existing results for the 3-LCBC by introducing a linear programming framework to optimize multicast opportunities across an arbitrary number of users. The proposed approach can be used to derive achievable scheme for the K-user coded caching problem with linear coded placement and scalar linear function retrieval, which was our original motivation to investigate the K-LCBC.