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In this work, we study the problem of linear index coding from graph homomorphism point of view. We show that the decision version of linear (scalar or vector) index coding problem is equivalent to certain graph homomorphism problem. Using this equivalence expression, we conclude the following results. First we introduce new lower bounds on linear index of graphs. Next, we show that if the linear index of a graph over a finite filed is bounded by a constant, then by changing the ground field, the linear index of the graph may change by at most a constant factor that is independent from the size of the graph. Finally, we show that the decision version of linear index coding problem is... 

The generalized belief propagation (GBP), introduced by Yedidia et al., is an extension of the belief propagation (BP) algorithm, which is widely used in different problems involved in calculating exact or approximate marginals of probability distributions. In many problems, it has been observed that the accuracy of GBP outperforms that of BP considerably. However, due to its generally higher complexity compared to BP, its application is limited in practice. In this paper, we introduce a stochastic version of GBP called stochastic generalized belief propagation (SGBP) that can be considered as an extension to the stochastic BP (SBP) algorithm introduced by Noorshams et al. They have shown... 

Recent empirical results have demonstrated that generalized belief propagation (GBP) can be used to closely estimate the capacity of certain 2D runlength-limited constraints. We provide a partial analytical validation of these observations by showing that GBP yields a lower bound on the partition function of 2D Ising models with restricted grid size. While previous papers have proved that belief propagation (BP) can be used to obtain a lower bound on the partition function of 2D Ising models, this paper is the first work that analyzes GBP-based partition function approximations of 2D Ising models  

We consider a group of mobile users, in closed proximity, who are interested in downloading a common content (e.g., a video file). We address a cooperative solution where each mobile device is equipped with both cellular and Wi-Fi interfaces. The users exploit the cellular link to download different shares of the content from the based-station and leverage on Wi-Fi link to exchange the received data. In order to expedite content delivery, the base-station transmits random linear network-coded data to users. This paper presents an analytical study of the average completion time, i.e., the time necessary for all devices to successfully retrieve the data. We propose an analytical model to... 

We consider the problem of private information retrieval (PIR) where a single user with private side information aims to retrieve multiple files from a library stored (uncoded) at a number of servers. We assume the side information at the user includes a subset of files stored privately (i.e., the server does not know the indices of these files). In addition, we require that the identity of requests and side information at the user are not revealed to any of the servers. The problem involves finding the minimum load to be transmitted from the servers to the user such that the requested files can be decoded with the help of received and side information. By providing matching lower and upper... 

Network traffic classification has become more important with the rapid growth of Internet and online applications. Numerous studies have been done on this topic which have led to many different approaches. Most of these approaches use predefined features extracted by an expert in order to classify network traffic. In contrast, in this study, we propose a deep learning-based approach which integrates both feature extraction and classification phases into one system. Our proposed scheme, called “Deep Packet,” can handle both traffic characterization in which the network traffic is categorized into major classes (e.g., FTP and P2P) and application identification in which identifying end-user... 

We consider an index coding problem in which several transmitters deliver distinct files to a number of users with minimum delay. Each user has access to a subset of other files from the library, which can be used as side information. The information sent by the transmitters experience a linear transformation before being received at the users. By benefiting from the concept of Zero-Forcing in MIMO systems, we generalize the notion of MinRank characterization and the clique cover algorithm to accommodate this generalized setting. We show that increasing the number of transmitters can substantially reduce the delivery delay. IEEE  

We consider an index coding problem in which several transmitters deliver distinct files to a number of users with minimum delay. Each user has access to a subset of other files from the library, which can be used as side information. The information sent by the transmitters experience a linear transformation before being received at the users. By benefiting from the concept of Zero-Forcing in MIMO systems, we generalize the notion of MinRank characterization and the clique cover algorithm to accommodate this generalized setting. We show that increasing the number of transmitters can substantially reduce the delivery delay. © 1997-2012 IEEE