An algebraic framework for end-to-end physical-layer network coding

TL;DR

This paper introduces an algebraic framework for physical-layer network coding using submodule transmission, defining a distance function, error correction, and exploring bounds and constructions for codes.

Contribution

It presents a novel algebraic approach to physical-layer network coding based on submodules, including new error-correcting code definitions and analysis methods.

Findings

Defined a distance function between modules related to information loss

Proposed a new class of submodule error-correcting codes

Investigated bounds and constructions for these codes

Abstract

We propose an algebraic setup for end-to-end physical-layer network coding based on submodule transmission. We introduce a distance function between modules, describe how it relates to information loss and errors, and show how to compute it. Then we propose a definition of submodule error-correcting code, and investigate bounds and constructions for such codes.