arXiv subjects

Haim H. Permuter

Publications and source records attributed to Haim H. Permuter.

45 records · Page 3Linked to original sources

arXiv2013

Universal Estimation of Directed Information

Four estimators of the directed information rate between a pair of jointly stationary ergodic finite-alphabet processes are proposed, based on universal probability assignments. The first one is a Shannon--McMillan--Breiman type estimator, similar to those used by Verdú (2005) and Cai, Kulkarni, and Verdú (2006) for estimation of other information measures. We show the almost sure and $L_1$ convergence properties of the estimator for any underlying universal probability assignment. The other three estimators map universal probability assignments to different functionals, each exhibiting relative merits such as smoothness, nonnegativity, and boundedness. We establish the consistency of these estimators in almost sure and $L_1$ senses, and derive near-optimal rates of convergence in the minimax sense under mild conditions. These estimators carry over directly to estimating other information measures of stationary ergodic finite-alphabet processes, such as entropy rate and mutual information rate, with near-optimal performance and provide alternatives to classical approaches in the existing literature. Guided by these theoretical results, the proposed estimators are implemented using the context-tree weighting algorithm as the universal probability assignment. Experiments on synthetic and real data are presented, demonstrating the potential of the proposed schemes in practice and the utility of directed information estimation in detecting and measuring causal influence and delay.

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arXiv2012

MAC with Action-Dependent State Information at One Encoder

Problems dealing with the ability to take an action that affects the states of state-dependent communication channels are of timely interest and importance. Therefore, we extend the study of action-dependent channels, which until now focused on point-to-point models, to multiple-access channels (MAC). In this paper, we consider a two-user, state-dependent MAC, in which one of the encoders, called the informed encoder, is allowed to take an action that affects the formation of the channel states. Two independent messages are to be sent through the channel: a common message known to both encoders and a private message known only to the informed encoder. In addition, the informed encoder has access to the sequence of channel states in a non-causal manner. Our framework generalizes previously evaluated settings of state dependent point-to-point channels with actions and MACs with common messages. We derive a single letter characterization of the capacity region for this setting. Using this general result, we obtain and compute the capacity region for the Gaussian action-dependent MAC. The unique methods used in solving the Gaussian case are then applied to obtain the capacity of the Gaussian action-dependent point-to-point channel; a problem was left open until this work. Finally, we establish some dualities between action-dependent channel coding and source coding problems. Specifically, we obtain a duality between the considered MAC setting and the rate distortion model known as "Successive Refinement with Actions". This is done by developing a set of simple duality principles that enable us to successfully evaluate the outcome of one problem given the other.

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arXiv2012

Directed Information, Causal Estimation, and Communication in Continuous Time

A notion of directed information between two continuous-time processes is proposed. A key component in the definition is taking an infimum over all possible partitions of the time interval, which plays a role no less significant than the supremum over "space" partitions inherent in the definition of mutual information. Properties and operational interpretations in estimation and communication are then established for the proposed notion of directed information. For the continuous-time additive white Gaussian noise channel, it is shown that Duncan's classical relationship between causal estimation and information continues to hold in the presence of feedback upon replacing mutual information by directed information. A parallel result is established for the Poisson channel. The utility of this relationship is then demonstrated in computing the directed information rate between the input and output processes of a continuous-time Poisson channel with feedback, where the channel input process is constrained to be constant between events at the channel output. Finally, the capacity of a wide class of continuous-time channels with feedback is established via directed information, characterizing the fundamental limit on reliable communication.

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arXiv2012

Information Embedding on Actions

The problem of optimal actuation for channel and source coding was recently formulated and solved in a number of relevant scenarios. In this class of models, actions are taken at encoders or decoders, either to acquire side information in an efficient way or to control or probe effectively the channel state. In this paper, the problem of embedding information on the actions is studied for both the source and the channel coding set-ups. In both cases, a decoder is present that observes only a function of the actions taken by an encoder or a decoder of an action-dependent point-to-point link. For the source coding model, this decoder wishes to reconstruct a lossy version of the source being transmitted over the point-to-point link, while for the channel coding problem the decoder wishes to retrieve a portion of the message conveyed over the link. For the problem of source coding with actions taken at the decoder, a single letter characterization of the set of all achievable tuples of rate, distortions at the two decoders and action cost is derived, under the assumption that the mentioned decoder observes a function of the actions non-causally, strictly causally or causally. A special case of the problem in which the actions are taken by the encoder is also solved. A single-letter characterization of the achievable capacity-cost region is then obtained for the channel coding set-up with actions. Examples are provided that shed light into the effect of information embedding on the actions for the action-dependent source and channel coding problems.

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arXiv2012

Source Coding When the Side Information May Be Delayed

For memoryless sources, delayed side information at the decoder does not improve the rate-distortion function. However, this is not the case for more general sources with memory, as demonstrated by a number of works focusing on the special case of (delayed) feedforward. In this paper, a setting is studied in which the encoder is potentially uncertain about the delay with which measurements of the side information are acquired at the decoder. Assuming a hidden Markov model for the sources, at first, a single-letter characterization is given for the set-up where the side information delay is arbitrary and known at the encoder, and the reconstruction at the destination is required to be (near) lossless. Then, with delay equal to zero or one source symbol, a single-letter characterization is given of the rate-distortion region for the case where side information may be delayed or not, unbeknownst to the encoder. The characterization is further extended to allow for additional information to be sent when the side information is not delayed. Finally, examples for binary and Gaussian sources are provided.

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arXiv2009

Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing

We investigate the role of Massey's directed information in portfolio theory, data compression, and statistics with causality constraints. In particular, we show that directed information is an upper bound on the increment in growth rates of optimal portfolios in a stock market due to {causal} side information. This upper bound is tight for gambling in a horse race, which is an extreme case of stock markets. Directed information also characterizes the value of {causal} side information in instantaneous compression and quantifies the benefit of {causal} inference in joint compression of two stochastic processes. In hypothesis testing, directed information evaluates the best error exponent for testing whether a random process $Y$ {causally} influences another process $X$ or not. These results give a natural interpretation of directed information $I(Y^n \to X^n)$ as the amount of information that a random sequence $Y^n = (Y_1,Y_2,..., Y_n)$ {causally} provides about another random sequence $X^n = (X_1,X_2,...,X_n)$. A new measure, {\em directed lautum information}, is also introduced and interpreted in portfolio theory, data compression, and hypothesis testing.

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arXiv2009

Source Coding with a Side Information "Vending Machine"

We study source coding in the presence of side information, when the system can take actions that affect the availability, quality, or nature of the side information. We begin by extending the Wyner-Ziv problem of source coding with decoder side information to the case where the decoder is allowed to choose actions affecting the side information. We then consider the setting where actions are taken by the encoder, based on its observation of the source. Actions may have costs that are commensurate with the quality of the side information they yield, and an overall per-symbol cost constraint may be imposed. We characterize the achievable tradeoffs between rate, distortion, and cost in some of these problem settings. Among our findings is the fact that even in the absence of a cost constraint, greedily choosing the action associated with the `best' side information is, in general, sub-optimal. A few examples are worked out.

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arXiv2008

New Bounds for the Capacity Region of the Finite-State Multiple Access Channel

The capacity region of the Finite-State Multiple Access Channel (FS-MAC) with feedback that may be an arbitrary time-invariant function of the channel output samples is considered. We provided a sequence of inner and outer bounds for this region. These bounds are shown to coincide, and hence yield the capacity region, of FS-MACs where the state process is stationary and ergodic and not affected by the inputs, and for indecomposable FS-MAC when feedback is not allowed. Though the capacity region is `multi-letter' in general, our results yield explicit conclusions when applied to specific scenarios of interest.

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arXiv2008

On Directed Information and Gambling

We study the problem of gambling in horse races with causal side information and show that Massey's directed information characterizes the increment in the maximum achievable capital growth rate due to the availability of side information. This result gives a natural interpretation of directed information $I(Y^n \to X^n)$ as the amount of information that $Y^n$ \emph{causally} provides about $X^n$. Extensions to stock market portfolio strategies and data compression with causal side information are also discussed.

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