Two-Unicast Two-Hop Interference Network: Finite-Field Model

TL;DR

This paper introduces a framework to convert finite-field multi-user channels into MIMO channels, enabling new coding schemes and achieving higher sum-rates in interference networks.

Contribution

The paper presents a novel framework for converting finite-field MACs into MIMO channels, facilitating advanced coding schemes for interference networks.

Findings

Achieves sum-rate of (2m-1) log p for 2x2x2 interference channel.

Establishes a relation between field extension and symbol extension.

Enables development of coding schemes similar to symbol extension in time-varying channels.

Abstract

In this paper we present a novel framework to convert the $K$-user multiple access channel (MAC) over $\FF_{p^m}$ into the $K$-user MAC over ground field $\FF_{p}$ with $m$ multiple inputs/outputs (MIMO). This framework makes it possible to develop coding schemes for MIMO channel as done in symbol extension for time-varying channel. Using aligned network diagonalization based on this framework, we show that the sum-rate of $(2m-1)\log{p}$ is achievable for a $2\times 2\times 2$ interference channel over $\FF_{p^m}$. We also provide some relation between field extension and symbol extension.