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Computable Bounds for Rate Distortion With Feed Forward for Stationary and Ergodic Sources
"... Abstract—In this paper, we consider the rate distortion problem of discretetime, ergodic, and stationary sources with feed forward at the receiver. We derive a sequence of achievable and computable rates that converge to the feedforward rate distortion. We show that for ergodic and stationary sour ..."
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Abstract—In this paper, we consider the rate distortion problem of discretetime, ergodic, and stationary sources with feed forward at the receiver. We derive a sequence of achievable and computable rates that converge to the feedforward rate distortion. We show that for ergodic and stationary sources, the rate is achievable for any, where the minimization is performed over the transition conditioning probability such that. We also show that the limit of exists and is the feedforward rate distortion. We follow Gallager’s proof where there is no feed forward and, with appropriate modification, obtain our result. We provide an algorithm for calculating using the alternating minimization procedure and present several numerical examples. We also present a dual form for the optimization of and transform it into a geometric programming problem. Index Terms—Alternating minimization procedure, Blahut–Arimoto (BA) algorithm, causal conditioning, concatenating code trees, directed information, ergodic and stationary sources, ergodic modes, geometric programming (GP), rate distortion with feed forward. I.
Capacity of the Discrete Memoryless Energy Harvesting Channel with Side Information
"... Abstract—We determine the capacity of a discrete memoryless communication channel with an energy harvesting transmitter and its battery state information available at the transmitter and the receiver. This capacity is an upper bound for the problem where side information is available only at the tra ..."
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Cited by 4 (4 self)
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Abstract—We determine the capacity of a discrete memoryless communication channel with an energy harvesting transmitter and its battery state information available at the transmitter and the receiver. This capacity is an upper bound for the problem where side information is available only at the transmitter. Since channel output feedback does not increase the capacity in this case, we equivalently study the resulting finitestate Markov channel with feedback. We express the capacity in terms of directed information. Additionally, we provide sufficient conditions under which the capacity expression is further simplified to include the stationary distribution of the battery state. We also obtain a singleletter expression for the capacity with battery state information at both sides and an infinitesized battery. Lastly, we consider achievable schemes when side information is available only at the transmitter for the case of an arbitrary finitesized battery. We numerically evaluate the capacity and achievable rates with and without receiver side information. I.
Capacity of a post channel with and without feedback
 in Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on, 2013
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Capacity and coding for the Ising channel with feedback. submitted to
 IEEE Trans. Inf. Theory. Available at
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Channel coding and source coding with increased partial side information
 in Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on
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1Directed Information Graphs
"... Abstract—We propose two graphical models to concisely represent causal influences between agents in a network. The first, the minimal generative model graph, reflects a minimal state space description of relationships. The second, the directed information graph, is a statistical approach similar to ..."
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Abstract—We propose two graphical models to concisely represent causal influences between agents in a network. The first, the minimal generative model graph, reflects a minimal state space description of relationships. The second, the directed information graph, is a statistical approach similar to conventional graphical models and uses directed information to generalize Granger causality. Although they are motivated differently, we show that under minimal assumptions, the graphs are equivalent. In order to identify the underlying graph, we present several algorithms. In general, joint statistics of the whole network are needed. We present an algorithm that uses the minimaldimension statistics necessary when upper bounds on the indegrees are known. In the event that the upperbounds are not valid, the result is nonetheless an optimal approximation. The algorithms require calculations of directed information. For the setting when directed information is estimated from data, we characterize the samplecomplexity of two directed information estimators. Their performance is similar to standard results for statistical estimation with iid data. When point estimates of directed information are not reliable, we compute confidence intervals. Furthermore, we propose an algorithm that uses confidence intervals to identify the best bounded indegree graph approximation that is robust to estimation error. Lastly, we demonstrate the effectiveness of the proposed algorithms through simulations and by identifying which news agencies influence which users in the Twitter network by analyzing only tweet times. The algorithms determine influences with high precision. Index Terms—Graphical models, network inference, causality, generative models, directed information.
1Analogy Between Gambling and MeasurementBased Work Extraction
"... In information theory, one area of interest is gambling, where mutual information characterizes the maximal gain in wealth growth rate due to knowledge of side information; the betting strategy that achieves this maximum is named the Kelly strategy. In the field of physics, it was recently shown tha ..."
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In information theory, one area of interest is gambling, where mutual information characterizes the maximal gain in wealth growth rate due to knowledge of side information; the betting strategy that achieves this maximum is named the Kelly strategy. In the field of physics, it was recently shown that mutual information can characterize the maximal amount of work that can be extracted from a single heat bath using measurementbased control protocols, i.e., using “information engines”. However, to the best of our knowledge, no relation between gambling and information engines has been presented before. In this paper, we briefly review the two concepts and then demonstrate an analogy between gambling, where bits are converted into wealth, and information engines, where bits representing measurements are converted into energy. From this analogy follows an extension of gambling to the continuousvalued case, which is shown to be useful for investments in currency exchange rates or in the stock market using options. Moreover, the analogy enables us to use wellknown methods and results from one field to solve problems in the other. We present three such cases: maximum work extraction when the probability distributions governing the system and measurements are unknown, work extraction when some energy is lost in each cycle, e.g., due to friction, and an analysis of systems with memory. In all three cases, the analogy enables us to use known results in order to obtain new ones.
CODING AND SCHEDULING IN ENERGY HARVESTING COMMUNICATION SYSTEMS
, 2014
"... Wireless networks composed of energy harvesting devices will introduce several transformative changes in wireless networking: energy selfsufficient, energy selfsustaining, perpetual operation; and an ability to deploy wireless networks at hardtoreach places such as remote rural areas, within the ..."
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Wireless networks composed of energy harvesting devices will introduce several transformative changes in wireless networking: energy selfsufficient, energy selfsustaining, perpetual operation; and an ability to deploy wireless networks at hardtoreach places such as remote rural areas, within the structures, and within the human body. Energy harvesting brings new dimensions to the wireless communication problem in the form of intermittency and randomness of available energy. In such systems, the communication mechanisms need to be designed by explicitly accounting for the energy harvesting constraints. In this dissertation, we investigate the effects of intermittency and randomness in the available energy for message transmission in energy harvesting communication systems. We use information theoretic and scheduling theoretic frameworks to determine the fundamental limits of communications with energy harvesting devices. We first investigate the information theoretic capacity of the single user Gaussian energy harvesting channel. In this problem, an energy harvesting transmitter with an unlimited sized battery communicates with a receiver over the classical