The Compute-and-Forward Protocol: Implementation and Practical Aspects

TL;DR

This paper explores the practical implementation of the Compute-and-Forward protocol for real Gaussian channels, linking rate maximization to lattice problems and proposing algorithms for efficient decoding.

Contribution

It provides a practical implementation framework for the Compute-and-Forward scheme, connecting rate optimization to lattice shortest vector problems and using Diophantine approximation algorithms.

Findings

Maximum likelihood decoding can be achieved via Diophantine approximation.

Implementation details for real Gaussian channels are provided.

The scheme's efficiency depends on solving lattice shortest vector problems.

Abstract

In a recent work, Nazer and Gastpar proposed the Compute-and-Forward strategy as a physical-layer network coding scheme. They described a code structure based on nested lattices whose algebraic structure makes the scheme reliable and efficient. In this work, we consider the implementation of their scheme for real Gaussian channels and one dimensional lattices. We relate the maximization of the transmission rate to the lattice shortest vector problem. We explicit, in this case, the maximum likelihood criterion and show that it can be implemented by using an Inhomogeneous Diophantine Approximation algorithm.