On the DoF of Two-way $2\times2\times2$ Relay Networks with or without Relay Caching

TL;DR

This paper analyzes the degrees of freedom in a two-way 2x2x2 relay network, showing caching can increase DoF from 8/3 to 4 in symmetric cases, revealing limits and potentials of bidirectional relay communication.

Contribution

It establishes the DoF bounds for two-way 2x2x2 relay networks and demonstrates how relay caching can enhance the DoF.

Findings

Without relay caching, DoF is bounded by 8/3.

Relay caching achieves the full 8/3 DoF.

Symmetric channel gains can yield a DoF of 4.

Abstract

Two-way relay is potentially an effective approach to spectrum sharing and aggregation by allowing simultaneous bidirectional transmissions between source-destinations pairs. This paper studies the two-way $2\times2\times2$ relay network, a class of four-unicast networks, where there are four source/destination nodes and two relay nodes, with each source sending a message to its destination. We show that without relay caching the total degrees of freedom (DoF) is bounded from above by $8/3$, indicating that bidirectional links do not double the DoF (It is known that the total DoF of one-way $2\times2\times2$ relay network is $2$.). Further, we show that the DoF of $8/3$ is achievable for the two-way $2\times2\times2$ relay network with relay caching. Finally, even though the DoF of this network is no more than $8/3$ for generic channel gains, DoF of $4$ can be achieved for a symmetric configuration of channel gains.