Classes of Delay-Independent Multimessage Multicast Networks with Zero-Delay Nodes

TL;DR

This paper characterizes the capacity regions of certain multimessage multicast networks with zero-delay nodes, showing that delay variations do not affect achievable rates in these network classes.

Contribution

It introduces a generalized-delay model for MMNs, derives capacity regions for three classes with zero-delay nodes, and proves delay independence of achievable rates.

Findings

Capacity regions are characterized for three classes of MMNs with zero-delay nodes.

Achievable rate sets are identical under classical and generalized-delay models for these classes.

Delay does not impact the set of achievable rates in the studied network classes.

Abstract

In a network, a node is said to incur a delay if its encoding of each transmitted symbol involves only its received symbols obtained before the time slot in which the transmitted symbol is sent (hence the transmitted symbol sent in a time slot cannot depend on the received symbol obtained in the same time slot). A node is said to incur no delay if its received symbol obtained in a time slot is available for encoding its transmitted symbol sent in the same time slot. Under the classical model, every node in the network incurs a delay. In this paper, we investigate the multimessage multicast network (MMN) under a generalized-delay model which allows some nodes to incur no delay. We obtain the capacity regions for three classes of MMNs with zero-delay nodes, namely the deterministic network dominated by product distribution, the MMN consisting of independent DMCs and the wireless erasure network. In addition, we show that for any MMN belonging to one of the above three classes, the set of achievable rate tuples under the generalized-delay model and under the classical model are the same, which implies that the set of achievable rate tuples for the MMN does not depend on the delay amounts incurred by the nodes in the network.