Compute-and-Forward: Finding the Best Equation

TL;DR

This paper presents a polynomial-time algorithm for solving the specific Shortest Lattice Vector problem arising in Compute-and-Forward, enabling optimal decoding of linear message combinations in interference channels.

Contribution

It introduces a deterministic, low-complexity algorithm to optimally solve the SLV problem specific to Compute-and-Forward, improving upon the general complexity of the problem.

Findings

The algorithm guarantees finding the optimal integer coefficients.

The approach reduces complexity from exponential to polynomial time.

It enhances the practical feasibility of Compute-and-Forward techniques.

Abstract

Compute-and-Forward is an emerging technique to deal with interference. It allows the receiver to decode a suitably chosen integer linear combination of the transmitted messages. The integer coefficients should be adapted to the channel fading state. Optimizing these coefficients is a Shortest Lattice Vector (SLV) problem. In general, the SLV problem is known to be prohibitively complex. In this paper, we show that the particular SLV instance resulting from the Compute-and-Forward problem can be solved in low polynomial complexity and give an explicit deterministic algorithm that is guaranteed to find the optimal solution.