Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations

TL;DR

This paper extends the compute-and-forward framework to include unequal powers, multiple linear combinations, and signal levels, unifying and generalizing recent results for improved network communication strategies.

Contribution

It introduces an expanded compute-and-forward framework that naturally incorporates unequal powers and multiple linear combinations through an intuitive signal level interpretation.

Findings

Unified recent achievability and optimality results.

Generalized framework for diverse network scenarios.

Enhanced decoding strategies for complex Gaussian networks.

Abstract

The compute-and-forward framework permits each receiver in a Gaussian network to directly decode a linear combination of the transmitted messages. The resulting linear combinations can then be employed as an end-to-end communication strategy for relaying, interference alignment, and other applications. Recent efforts have demonstrated the advantages of employing unequal powers at the transmitters and decoding more than one linear combination at each receiver. However, neither of these techniques fit naturally within the original formulation of compute-and-forward. This paper proposes an expanded compute-and-forward framework that incorporates both of these possibilities and permits an intuitive interpretation in terms of signal levels. Within this framework, recent achievability and optimality results are unified and generalized.