Hierarchical Models for Relational Event Sequences

Interaction within small groups can often be represented as a sequence of events, where each event involves a sender and a recipient. Recent methods for modeling network data in continuous time model the rate at which individuals interact conditioned on the previous history of events as well as actor covariates. We present a hierarchical extension for modeling multiple such sequences, facilitating inferences about event-level dynamics and their variation across sequences. The hierarchical approach allows one to share information across sequences in a principled manner---we illustrate the efficacy of such sharing through a set of prediction experiments. After discussing methods for adequacy checking and model selection for this class of models, the method is illustrated with an analysis of high school classroom dynamics

Formal analysis techniques for gossiping protocols

We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them

Achievable rate region for three user discrete broadcast channel based on coset codes

We present an achievable rate region for the general three user discrete memoryless broadcast channel, based on nested coset codes. We characterize 3-to-1 discrete broadcast channels, a class of broadcast channels for which the best known coding technique\footnote{We henceforth refer to this as Marton's coding for three user discrete broadcast channel.}, which is obtained by a natural generalization of that proposed by Marton for the general two user discrete broadcast channel, is strictly sub-optimal. In particular, we identify a novel 3-to-1 discrete broadcast channel for which Marton's coding is \textit{analytically} proved to be strictly suboptimal. We present achievable rate regions for the general 3-to-1 discrete broadcast channels, based on nested coset codes, that strictly enlarge Marton's rate region for the aforementioned channel. We generalize this to present achievable rate region for the general three user discrete broadcast channel. Combining together Marton's coding and that proposed herein, we propose the best known coding technique, for a general three user discrete broadcast channel.Comment: A non-additive 3-user discrete broadcast channel is identified for which achievable rate region based on coset codes is analytically proven to be strictly larger than that achievable using unstructured iid codes. This version is submitted to IEEE Transactions on Information Theor

Secrecy Capacity of a Class of Broadcast Channels with an Eavesdropper

We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. We consider several special classes of channels. As the first model, we consider the degraded multi-receiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multi-receiver wiretap channel with a less noisiness order in each sub-channel, where this order is not necessarily the same for all sub-channels. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a special class of degraded parallel multi-receiver wiretap channels and provide a stronger result. In particular, we study the case with two sub-channels two users and one eavesdropper, where there is a degradedness order in each sub-channel such that in the first (resp. second) sub-channel the second (resp. first) receiver is degraded with respect to the first (resp. second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both sub-channels. We determine the secrecy capacity region of this channel. Finally, we focus on a variant of this previous channel model where the transmitter can use only one of the sub-channels at any time. We characterize the secrecy capacity region of this channel as well.Comment: Submitted to EURASIP Journal on Wireless Communications and Networking (Special Issue on Wireless Physical Layer Security

Scheduling of Multicast and Unicast Services under Limited Feedback by using Rateless Codes

Many opportunistic scheduling techniques are impractical because they require accurate channel state information (CSI) at the transmitter. In this paper, we investigate the scheduling of unicast and multicast services in a downlink network with a very limited amount of feedback information. Specifically, unicast users send imperfect (or no) CSI and infrequent acknowledgements (ACKs) to a base station, and multicast users only report infrequent ACKs to avoid feedback implosion. We consider the use of physical-layer rateless codes, which not only combats channel uncertainty, but also reduces the overhead of ACK feedback. A joint scheduling and power allocation scheme is developed to realize multiuser diversity gain for unicast service and multicast gain for multicast service. We prove that our scheme achieves a near-optimal throughput region. Our simulation results show that our scheme significantly improves the network throughput over schemes employing fixed-rate codes or using only unicast communications

Comparison of Channels: Criteria for Domination by a Symmetric Channel

This paper studies the basic question of whether a given channel $V$ can be dominated (in the precise sense of being more noisy) by a $q$-ary symmetric channel. The concept of "less noisy" relation between channels originated in network information theory (broadcast channels) and is defined in terms of mutual information or Kullback-Leibler divergence. We provide an equivalent characterization in terms of $\chi^2$-divergence. Furthermore, we develop a simple criterion for domination by a $q$-ary symmetric channel in terms of the minimum entry of the stochastic matrix defining the channel $V$. The criterion is strengthened for the special case of additive noise channels over finite Abelian groups. Finally, it is shown that domination by a symmetric channel implies (via comparison of Dirichlet forms) a logarithmic Sobolev inequality for the original channel.Comment: 31 pages, 2 figures. Presented at 2017 IEEE International Symposium on Information Theory (ISIT