Causal relay networks

TL;DR

This paper investigates causal relay networks with both strictly causal and causal relays, deriving new bounds and demonstrating achievable strategies that improve understanding of network capacity.

Contribution

It introduces two novel cut-set bounds for causal relay networks and shows their achievability using simple amplify-and-forward strategies.

Findings

New cut-set bounds for causal relay networks

Achievability of bounds with amplify-and-forward relaying

Improved capacity results for causal relay channels

Abstract

In this paper, we study causal discrete-memoryless relay networks (DMRNs). The network consists of multiple nodes, each of which can be a source, relay, and/or destination. In the network, there are two types of relays, i.e., relays with one sample delay (strictly causal) and relays without delay (causal) whose transmit signal depends not only on the past received symbols but also on the current received symbol. For this network, we derive two new cut-set bounds, one when the causal relays have their own messages and the other when not. Using examples of a causal vector Gaussian two-way relay channel and a causal vector Gaussian relay channel, we show that the new cut-set bounds can be achieved by a simple amplify-and-forward type relaying. Our result for the causal relay channel strengthens the previously known capacity result for the same channel by El Gamal, Hassanpour, and Mammen.