Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error probabilities for various problems are bounded above by a non-vanishing constant and the spotlight is shone on achievable coding rates as functions of the growing blocklengths. This represents the study of asymptotic estimates with non-vanishing error probabilities. In Part I, after reviewing the fundamentals of information theory, we discuss Strassen's seminal result for binary hypothesis testing where the type-I error probability is non-vanishing and the rate of decay of the type-II error probability with growing number of independent observations is characterized. In Part II, we use this basic hypothesis testing result to develop second- and sometimes, even third-order asymptotic expansions for point-to-point communication. Finally in Part III, we consider network information theory problems for which the second-order asymptotics are known. These problems include some classes of channels with random state, the multiple-encoder distributed lossless source coding (Slepian-Wolf) problem and special cases of the Gaussian interference and multiple-access channels. Finally, we discuss avenues for further research.Comment: Further comments welcom

On the capacity of multiple input erasure relay channels: The Non-degraded case

We consider in this paper a network that consists of two senders and two receivers. We further assume that each sender could act as a relay for other communications. All channels connecting these nodes are supposed to be erasure channels where symbols are received correctly (error-free), or lost. This model is realistic for many practical scenarios in the context of wireless and sensor networks. In a previous works, we have addressed the capacity region of this network under physically degraded hypothesis. The non-degraded case is addressed in this paper. We derive a capacity bound for the proposed network and we show that it can be reached through a practical coding scheme based on MDS codes. We make also a comparison of the achieved rates compared to a simple time sharing of single sender relay channels

An information theory for erasure channels (invited paper)

In this paper we present a rapid review of known results in the context of different scenario of the erasure channel. We will also give a converse capacity bound for relay channel showing that the cut-set bound is not attainable in general by any fixed coding scheme for the single sender-single relay case. This bound shows the difference between the degraded situation where the cut-set bound is attainable and some specific case of the non-degraded situation where the cut-set bound is not attainable. The obtained reverse bound could be used for deriving tighter cut-set type bound for general multi-terminal erasure channels

A new relaying scheme for cheap wireless relay nodes

In this paper we will propose a relaying scheme for wireless multi-hop networks. It is based on collaboration of intermediate relays at network layer to forward useful side information in place of dumbly forwarding packets. In our scheme we assume that the nodes are not able to benefit from any interference cancellation mechanism. The channels from sender to relay nodes and from sender to receiver are logically separated through a temporal scheduling. This model is realistic for many practical scenarios in the context of wireless networks. We will show in this paper the information theoretic bounds and show that they are achievable using practical codes. The proposed coding scheme is simulated in realistic scenarios. The obtained results show a remarkable improvement in throughput, relay load and reliability compared to network using classical routing approach

Advanced machine learning approaches for target detection, tracking and recognition

This dissertation addresses the key technical components of an Automatic Target Recognition (ATR) system namely: target detection, tracking, learning and recognition. Novel solutions are proposed for each component of the ATR system based on several new advances in the field of computer vision and machine learning. Firstly, we introduce a simple and elegant feature, RelCom, and a boosted feature selection method to achieve a very low computational complexity target detector. Secondly, we present a particle filter based target tracking algorithm that uses a quad histogram based appearance model along with online feature selection. Further, we improve the tracking performance by means of online appearance learning where appearance learning is cast as an Adaptive Kalman filtering (AKF) problem which we formulate using both covariance matching and, for the first time in a visual tracking application, the recent autocovariance least-squares (ALS) method. Then, we introduce an integrated tracking and recognition system that uses two generative models to accommodate the pose variations and maneuverability of different ground targets. Specifically, a tensor-based generative model is used for multi-view target representation that can synthesize unseen poses, and can be trained from a small set of signatures. In addition, a target-dependent kinematic model is invoked to characterize the target dynamics. Both generative models are integrated in a graphical framework for joint estimation of the target's kinematics, pose, and discrete valued identity. Finally, for target recognition we advocate the concept of a continuous identity manifold that captures both inter-class and intra-class shape variability among training targets. A hemispherical view manifold is used for modeling the view-dependent appearance. In addition to being able to deal with arbitrary view variations, this model can determine the target identity at both class and sub-class levels, for targets not present in the training data. The proposed components of the ATR system enable us to perform low computational complexity target detection with low false alarm rates, robust tracking of targets under challenging circumstances and recognition of target identities at both class and sub-class levels. Experiments on real and simulated data confirm the performance of the proposed components with promising results

When all information is not created equal

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 191-196).Following Shannon's landmark paper, the classical theoretical framework for communication is based on a simplifying assumption that all information is equally important, thus aiming to provide a uniform protection to all information. However, this homogeneous view of information is not suitable for a variety of modern-day communication scenarios such as wireless and sensor networks, video transmission, interactive systems, and control applications. For example, an emergency alarm from a sensor network needs more protection than other transmitted information. Similarly, the coarse resolution of an image needs better protection than its finer details. For such heterogeneous information, if providing a uniformly high protection level to all parts of the information is infeasible, it is desirable to provide different protection levels based on the importance of those parts. The main objective of this thesis is to extend classical information theory to address this heterogeneous nature of information. Many theoretical tools needed for this are fundamentally different from the conventional homogeneous setting. One key issue is that bits are no more a sufficient measure of information. We develop a general framework for understanding the fundamental limits of transmitting such information, calculate such fundamental limits, and provide optimal architectures for achieving these limits. Our analysis shows that even without sacrificing the data-rate from channel capacity, some crucial parts of information can be protected with exponential reliability. This research would challenge the notion that a set of homogenous bits should necessarily be viewed as a universal interface to the physical layer; this potentially impacts the design of network architectures. This thesis also develops two novel approaches for simplifying such difficult problems in information theory. Our formulations are based on ideas from graphical models and Euclidean geometry and provide canonical examples for network information theory. They provide fresh insights into previously intractable problems as well as generalize previous related results.by Shashibhushan Prataprao Borade.Ph.D