Delay Scaling Law of Random Wireless Networks: Impact of Blocklength

In this thesis we focus on an important aspect of all communication networks, the delay. We measure the delay through the blocklength, which is one of the most basic quantities in information theory. By studying the interplay between number of users and blocklength, we characterize the delay scaling. The result is fundamental and is derived from one-shot bounds. We consider the simplest multihopping scheme, where each message is relayed several times. The effect of error propagation is characterized and the optimal strategy when using multihopping scheme is derived. We also came up with a more general version of the multihopping scheme, the time-division multiaccess multihopping scheme, which has the potential to be extended to model practical networks. The contribution of this thesis is to find the delay scaling of the multihopping scheme. In an network with 2k randomly one-to-one paired users and area k, assume a source with F(k) bits to send, we show that the delay is Θ(√kF (k)) if F (k) = Ω(√klog k); and is Θ(k log k) if F(k) = o(√klog k). This is derived by studying the limit of the multihopping scheme for large networks. We derive theoretically lower and upper bounds from the most fundamental one-shot results to characterize the blocklength constraint for the network. The result indicates the necessary and sufficient condition on the network blocklength scaling is ω(√klog k).