相关论文: Entropy vectors and network codes

In secure network coding, there is a possibility that the eavesdropper can improve her performance when she changes (contaminates) the information on the attacked edges (active attack) and chooses the attacked edges adaptively (adaptive…

We discuss linear programming techniques that help to deduce corollaries of non classic inequalities for Shannon's entropy. We focus on direct applications of the copy lemma. These applications involve implicitly some (known or unknown)…

The extremal inequality approach plays a key role in network information theory problems. In this paper, we propose a novel monotone path construction in product probability space. The optimality of Gaussian distribution is then established…

In index coding, a server broadcasts multiple messages to their respective receivers, each with some side information that can be utilized to reduce the amount of communication from the server. Distributed index coding is an extension of…

For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…

The capacity of a class of multi-way relay channels, where L users communicate via a relay (at possibly different rates), is derived for the case where the channel outputs are modular sums of the channel inputs and the receiver noise. The…

A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum $\rho$-th moment of the number of performed…

This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues…

Recently, it has been shown that the max flow capacity can be achieved in a multicast network using network coding. In this paper, we propose and analyze a more realistic model for wireless random networks. We prove that the capacity of…

In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…

Satellite networks provide unique challenges that can restrict users' quality of service. For example, high packet erasure rates and large latencies can cause significant disruptions to applications such as video streaming or voice-over-IP.…

We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type…

Nonextensivity is foreseeable in network ensembles, as heterogeneous interactions generally exist in complex networked systems that need to be described by network ensembles. But this nonextensivity has not been literatured proved yet. In…

We study a quantity called discrete layered entropy, which approximates the Shannon entropy within a logarithmic gap. Compared to the Shannon entropy, the discrete layered entropy is piecewise linear, approximates the expected length of the…

We establish a connection between barcode entropy and metric entropy. Namely, we show that the barcode entropy bounds the metric entropy from below for a measure from a specific class of invariant measures associated with a pair of…

We define a notion of network capacity region of networks that generalizes the notion of network capacity defined by Cannons et al. and prove its notable properties such as closedness, boundedness and convexity when the finite field is…

Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…

Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when…

In this paper from communication channel coding perspective we are able to present both a theoretical and practical discussion of AI's uncertainty, capacity and evolution for pattern classification based on the classical Rademacher…

A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum $\rho$-th moment of the number of performed…