Sum-GDoF of Symmetric Multi-hop Interference Channel under Finite Precision CSIT using Aligned-Images Sumset Inequalities

TL;DR

This paper characterizes the sum-GDoF of symmetric multi-hop interference channels under finite precision CSIT, showing that simple, robust schemes are GDoF optimal and that benefits of fragile schemes vanish in this setting.

Contribution

It provides the first GDoF characterization for multi-hop interference channels with finite precision CSIT, demonstrating the optimality of simple rate-splitting schemes.

Findings

Sum-GDoF remains unchanged even with perfect CSIT in the first hop.

For large number of hops, GDoF approaches that of a one-hop broadcast channel.

Simple rate-splitting schemes are GDoF optimal under finite precision CSIT.

Abstract

Aligned-Images Sumset Inequalities are used in this work to study the Generalized Degrees of Freedom (GDoF) of the symmetric layered multi-hop interference channel under the robust assumption that the channel state information at the transmitters (CSIT) is limited to finite precision. First, the sum-GDoF value is characterized for the $2\times 2\times 2$ setting that is comprised of $2$ sources, $2$ relays, and $2$ destinations. It is shown that the sum-GDoF do not improve even if perfect CSIT is allowed in the first hop, as long as the CSIT in the second hop is limited to finite precision. The sum GDoF characterization is then generalized to the $2\times 2\times \cdots \times 2$ setting that is comprised of $L$ hops. Remarkably, for large $L$, the GDoF value approaches that of the one hop broadcast channel that is obtained by full cooperation among the two transmitters of the last hop, with finite precision CSIT. Previous studies of multi-hop interference networks either identified sophisticated GDoF optimal schemes under perfect CSIT, such as aligned interference neutralization and network diagonalization, that are powerful in theory but too fragile to be practical, or studied robust achievable schemes like classical amplify/decode/compress-and-forward without claims of information-theoretic optimality. In contrast, under finite precision CSIT, we show that the benefits of fragile schemes are lost, while a combination of classical random coding schemes that are simpler and much more robust, namely a rate-splitting between decode-and-forward and amplify-and-forward, is shown to be GDoF optimal. As such, this work represents another step towards bridging the gap between theory (optimality) and practice (robustness) with the aid of Aligned-Images Sumset Inequalities.