On dependence and delay: Capacity bounds for wireless networks

Abstract

This paper investigates the impact of noise dependence and signal delay on the capacities of networks. It is shown that statistical dependence between the noise in a network's component channels is helpful for communication. In particular, the capacity region of a network whose component channels exhibit dependent noise is a superset of the capacity region of a network built from the same component channels when the noise in those channels is independent. It is also shown that delay has no impact on capacity. That is, the capacity of a network of memoryless channels is unchanged by the addition of finite delays anywhere in the network. Both results are proven for all possible networks of memoryless point-to-point and multi-terminal channels under multiple multicast connections. All other connection types (e.g., single unicast, multiple unicast, single multicast, and mixed unicast and multicast connections) are special cases of the multiple multicast problem, and are therefore included in the given results. The results also generalize from reliable communication of independent sources to lossy or lossy description of possibly dependent sources (i.e., joint source-channel coding) across the same network.