Degrees-of-Freedom of the MIMO Three-Way Channel with Node-Intermittency

TL;DR

This paper investigates the degrees-of-freedom limits of MIMO three-way channels with intermittent nodes, introducing a non-adaptive scheme that is optimal for sum-DoF but highlighting the need for adaptive schemes to achieve the full DoF region.

Contribution

It introduces a non-adaptive encoding scheme for intermittent MIMO three-way channels and characterizes its optimality for sum-DoF, while demonstrating the necessity of adaptive schemes for the full DoF region.

Findings

Non-adaptive scheme achieves sum-DoF optimality.

Adaptive schemes are necessary for the full DoF region.

Characterization of DoF limits in intermittent multi-way channels.

Abstract

The characterization of fundamental performance bounds of many-to-many communication systems in which participating nodes are active in an intermittent way is one of the major challenges in communication theory. In order to address this issue, we introduce the multiple-input multiple-output (MIMO) three-way channel (3WC) with an intermittent node and study its degrees-of-freedom (DoF) region and sum-DoF. We devise a non-adaptive encoding scheme based on zero-forcing, interference alignment and erasure coding, and show its DoF region (and thus sum-DoF) optimality for non-intermittent 3WCs and its sum-DoF optimality for (node-)intermittent 3WCs. However, we show by example that in general some DoF tuples in the intermittent 3WC can only be achieved by adaptive schemes, such as decode-forward relaying. This shows that non-adaptive encoding is sufficient for the non-intermittent 3WC and for the sum-DoF of intermittent 3WCs, but adaptive encoding is necessary for the DoF region of intermittent 3WCs. Our work contributes to a better understanding of the fundamental limits of multi-way communication systems with intermittency and the impact of adaptation therein.