A Low-Complexity Message Recovery Method for Compute-and-Forward Relaying

TL;DR

This paper proposes a low-complexity message recovery method for Compute-and-Forward relaying that guarantees system solvability by carefully designing relay equation sets, without requiring relay communication.

Contribution

It introduces a novel relay selection strategy that ensures solvability of the message system while maintaining high computation rates, with constant complexity and no relay communication.

Findings

Guaranteed solvability of message system with designed equation sets

Maintains high computation rates despite constraints

Achieves low computational complexity

Abstract

The Compute-and-Forward relaying strategy achieves high computation rates by decoding linear combinations of transmitted messages at intermediate relays. However, if the involved relays independently choose which combinations of the messages to decode, there is no guarantee that the overall system of linear equations is solvable at the destination. In this article it is shown that, for a Gaussian fading channel model with two transmitters and two relays, always choosing the combination that maximizes the computation rate often leads to a case where the original messages cannot be recovered. It is further shown that by limiting the relays to select from carefully designed sets of equations, a solvable system can be guaranteed while maintaining high computation rates. The proposed method has a constant computational complexity and requires no information exchange between the relays.