Compute and Forward: End to End Performance over Residue Class Signal Constellation

TL;DR

This paper presents a practical implementation and analysis of compute and forward over residue class signal constellations, focusing on error probability bounds and the impact of matrix rank on performance.

Contribution

It introduces a Gaussian integer lattice-based signal model and derives error probability bounds, highlighting the importance of full rank matrices at the destination.

Findings

Error probability bounds are derived and validated through simulations.

Performance is limited by the full rank condition of the coefficient matrix.

Decoding functions are provided for relay and destination nodes.

Abstract

In this letter, the problem of implementing compute and forward (CF) is addressed. We present a practical signal model to implement CF which is built on the basis of Gaussian integer lattice partitions. We provide practical decoding functions at both relay and destination nodes thereby providing a framework for complete analysis of CF. Our main result is the analytical derivation and simulations based validation of union bound of probability of error for end to end performance of CF. We show that the performance is not limited by the linear combination decoding at the relay but by the full rank requirement of the coefficient matrix at the destination.