/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

Network Information Theory

Information Theory and Reliable Communication

(1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

https://link.springer.com/content/pdf/10.1057%2Fjors.1987.184.pdf

Applied Probability and Queues

Convex Analysis: (pms-28)

A study of Gaussian mixture models of color and texture features for image classification and segmentation

We develop elements of a theory of cooperation and coordination in networks. Rather than considering a communication network as a means of distributing information, or of reconstructing random processes at remote nodes, we ask what dependence can be established among the nodes given the communication constraints. Specifically, in a network with communication rates {Ri,j} between the nodes, we ask what is the set of all achievable joint distributions p(x1, ..., xm) of actions at the nodes of the network. Several networks are solved, including arbitrarily large cascade networks. Distributed cooperation can be the solution to many problems such as distributed games, distributed control, and establishing mutual information bounds on the influence of one part of a physical system on another.

Coordination Capacity

We consider capacity of discrete-time channels with feedback for the general case where the feedback is a time-invariant deterministic function of the output samples. Under the assumption that the channel states take values in a finite alphabet, we find a sequence of achievable rates and a sequence of upper bounds on the capacity. The achievable rates and the upper bounds are computable for any N, and the limits of the sequences exist. We show that when the probability of the initial state is positive for all the channel states, then the capacity is the limit of the achievable-rate sequence. We further show that when the channel is stationary, indecomposable, and has no intersymbol interference (ISI), its capacity is given by the limit of the maximum of the (normalized) directed information between the input XN and the output YN, i.e., C=limNrarrinfin(1/n)max I(XNrarrYN) where the maximization is taken over the causal conditioning probability Q(xNparzN-1) defined in this paper. The main idea for obtaining the results is to add causality into Gallager's results on finite state channels. The capacity results are used to show that the source-channel separation theorem holds for time-invariant determinist feedback, and if the state of the channel is known both at the encoder and the decoder, then feedback does not increase capacity.

Finite State Channels With Time-Invariant Deterministic Feedback

We establish that the feedback capacity of the trapdoor channel is the logarithm of the golden ratio and provide a simple communication scheme that achieves capacity. As part of the analysis, we formulate a class of dynamic programs that characterize capacities of unifilar finite-state channels. The trapdoor channel is an instance that admits a simple closed-form solution.

/pdf/capacity-of-the-trapdoor-channel-with-feedback-1s90kahdqj.pdf

Capacity of the Trapdoor Channel With Feedback

We consider capacity of discrete-time channels with feedback for the general case where the feedback is a time-invariant deterministic function of the output samples. Under the assumption that the channel states take values in a finite alphabet, we find an achievable rate and an upper bound on the capacity. We further show that when the channel is indecomposable, and has no intersymbol interference (ISI), its capacity is given by the limit of the maximum of the (normalized) directed information between the input $X^N$ and the output $Y^N$, i.e. $C = \lim_{N \to \infty} \frac{1}{N} \max I(X^N \to Y^N)$, where the maximization is taken over the causal conditioning probability $Q(x^N||z^{N-1})$ defined in this paper. The capacity result is used to show that the source-channel separation theorem holds for time-invariant determinist feedback. We also show that if the state of the channel is known both at the encoder and the decoder then feedback does not increase capacity.

Haim H. Permuter

Papers

A study of Gaussian mixture models of color and texture features for image classification and segmentation

Coordination Capacity

Finite State Channels With Time-Invariant Deterministic Feedback

Capacity of the Trapdoor Channel With Feedback

Finite State Channels with Time-Invariant Deterministic Feedback