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Amin Gohari

Publications and source records attributed to Amin Gohari.

At least 55 records · Page 3Linked to original sources
arXiv2017

On the Capacity of a Class of Signal-Dependent Noise Channels

In some applications, the variance of additive measurement noise depends on the signal that we aim to measure. For instance, additive Gaussian signal-dependent noise (AGSDN) channel models are used in molecular and optical communication. Herein we provide lower and upper bounds on the capacity of additive signal-dependent noise (ASDN) channels. The idea of the first lower bound is the extension of the majorization inequality, and for the second one, it uses some calculations based on the fact that $h(Y) > h (Y|Z)$. Both of them are valid for all additive signal-dependent noise (ASDN) channels defined in the paper. The upper bound is based on a previous idea of the authors ("symmetric relative entropy") and is used for the additive Gaussian signal-dependent noise (AGSDN) channels. These bounds indicate that in ASDN channels (unlike the classical AWGN channels), the capacity does not necessarily become larger by making the variance function of the noise smaller. We also provide sufficient conditions under which the capacity becomes infinity. This is complemented by a number of conditions that imply capacity is finite and a unique capacity achieving measure exists (in the sense of the output measure).

cs.IT↗
arXiv2017

Existence and Continuity of Differential Entropy for a Class of Distributions

In this paper, we identify a class of absolutely continuous probability distributions, and show that the differential entropy is uniformly convergent over this space under the metric of total variation distance. One of the advantages of this class is that the requirements could be readily verified for a given distribution.

cs.IT↗
arXiv2017

Quantum Achievability Proof via Collision Relative Entropy

In this paper, we provide a simple framework for deriving one-shot achievable bounds for some problems in quantum information theory. Our framework is based on the joint convexity of the exponential of the collision relative entropy, and is a (partial) quantum generalization of the technique of Yassaee et al. (2013) from classical information theory. Based on this framework, we derive one-shot achievable bounds for the problems of communication over classical-quantum channels, quantum hypothesis testing, and classical data compression with quantum side information. We argue that our one-shot achievable bounds are strong enough to give the asymptotic achievable rates of these problems even up to the second order.

quant-ph↗
arXiv2017

Monotone Measures for Non-Local Correlations

Non-locality is the phenomenon of observing strong correlations among the outcomes of local measurements of a multipartite physical system. No-signaling boxes are the abstract objects for studying non-locality, and wirings are local operations on the space of no-signaling boxes. This means that, no matter how non-local the nature is, the set of physical non-local correlations must be closed under wirings. Then, one approach to identify the non-locality of nature is to characterize closed sets of non-local correlations. Although non-trivial examples of wirings of no-signaling boxes are known, there is no systematic way to study wirings. In particular, given a set of no-signaling boxes, we do not know a general method to prove that it is closed under wirings. In this paper, we propose the first general method to construct such closed sets of non-local correlations. We show that a well-known measure of correlation, called maximal correlation, when appropriately defined for non-local correlations, is monotonically decreasing under wirings. This establishes a conjecture about the impossibility of simulating isotropic boxes from each other, implying the existence of a continuum of closed sets of non-local boxes under wirings. To prove our main result, we introduce some mathematical tools that may be of independent interest: we define a notion of maximal correlation ribbon as a generalization of maximal correlation, and provide a connection between it and a known object called hypercontractivity ribbon; we show that these two ribbons are monotone under wirings too.

quant-ph↗
arXiv2016

Type Based Sign Modulation and its Application for ISI mitigation in Molecular Communication

An important challenge in design of modulation schemes for molecular communication is positivity of the transmission signal (only a positive concentration of molecules can be released in the environment). This restriction makes handling of the InterSymbol Interference (ISI) a challenge for molecular communication. Previous works have proposed use of chemical reactions to remove molecules from the environment, and to effectively simulate negative signals. However, the differential equation describing a diffusion-reaction process is non-linear. This precludes the possibility of using Fourier transform tools. In this paper, a solution for simulating negative signals based on the diffusion-reaction channel model is proposed. While the proposed solution does not exploit the full degrees of freedom available for signaling in a diffusion-reaction process, but its end-to-end system is a linear channel and amenable to Fourier transform analysis. Based on our solution, a modulation scheme and a precoder are introduced and shown to have a significant reduction in error probability compared to previous modulation schemes such as CSK and MCSK. The effect of various imperfections (such as quantization error) on the communication system performance are studied.

cs.IT↗
arXiv2016

Information Theory of Molecular Communication: Directions and Challenges

Molecular Communication (MC) is a communication strategy that uses molecules as carriers of information, and is widely used by biological cells. As an interdisciplinary topic, it has been studied by biologists, communication theorists and a growing number of information theorists. This paper aims to specifically bring MC to the attention of information theorists. To do this, we first highlight the unique mathematical challenges of studying the capacity of molecular channels. Addressing these problems require use of known, or development of new mathematical tools. Toward this goal, we review a subjective selection of the existing literature on information theoretic aspect of molecular communication. The emphasis here is on the mathematical techniques used, rather than on the setup or modeling of a specific paper. Finally, as an example, we propose a concrete information theoretic problem that was motivated by our study of molecular communication.

cs.IT↗
arXiv2016

Simulation of a Channel with Another Channel

In this paper, we study the problem of simulating a DMC channel from another DMC channel under an average-case and an exact model. We present several achievability and infeasibility results, with tight characterizations in special cases. In particular for the exact model, we fully characterize when a BSC channel can be simulated from a BEC channel when there is no shared randomness. We also provide infeasibility and achievability results for simulation of a binary channel from another binary channel in the case of no shared randomness. To do this, we use properties of Rényi capacity of a given order. We also introduce a notion of "channel diameter" which is shown to be additive and satisfy a data processing inequality.

cs.IT↗
arXiv2016

On the Duality of Additivity and Tensorization

A function is said to be additive if, similar to mutual information, expands by a factor of $n$, when evaluated on $n$ i.i.d. repetitions of a source or channel. On the other hand, a function is said to satisfy the tensorization property if it remains unchanged when evaluated on i.i.d. repetitions. Additive rate regions are of fundamental importance in network information theory, serving as capacity regions or upper bounds thereof. Tensorizing measures of correlation have also found applications in distributed source and channel coding problems as well as the distribution simulation problem. Prior to our work only two measures of correlation, namely the hypercontractivity ribbon and maximal correlation (and their derivatives), were known to have the tensorization property. In this paper, we provide a general framework to obtain a region with the tensorization property from any additive rate region. We observe that hypercontractivity ribbon indeed comes from the dual of the rate region of the Gray-Wyner source coding problem, and generalize it to the multipartite case. Then we define other measures of correlation with similar properties from other source coding problems. We also present some applications of our results.

cs.IT↗
arXiv2016

Phi-Entropic Measures of Correlation

A measure of correlation is said to have the tensorization property if it is unchanged when computed for i.i.d.\ copies. More precisely, a measure of correlation between two random variables $(X, Y)$ denoted by $ρ(X, Y)$, has the tensorization property if $ρ(X^n, Y^n)=ρ(X, Y)$ where $(X^n, Y^n)$ is $n$ i.i.d.\ copies of $(X, Y)$.Two well-known examples of such measures are the maximal correlation and the hypercontractivity ribbon (HC~ribbon). We show that the maximal correlation and HC ribbons are special cases of $Φ$-ribbon, defined in this paper for any function $Φ$ from a class of convex functions ($Φ$-ribbon reduces to HC~ribbon and the maximal correlation for special choices of $Φ$). Any $Φ$-ribbon is shown to be a measures of correlation with the tensorization property. We show that the $Φ$-ribbon also characterizes the $Φ$-strong data processing inequality constant introduced by Raginsky. We further study the $Φ$-ribbon for the choice of $Φ(t)=t^2$ and introduce an equivalent characterization of this ribbon.

cs.IT↗
arXiv2016

On the Monotone Measure of Correlation

Based on the notion of maximal correlation, Kimeldorf, May and Sampson (1980) introduce a measure of correlation between two random variables, called the "concordant monotone correlation" (CMC). We revisit, generalize and prove new properties of this measure of correlation. It is shown that CMC captures various types of correlation detected in measures of rank correlation like the Kendall tau correlation. We show that the CMC satisfies the data processing and tensorization properties (that make ordinary maximal correlation applicable to problems in information theory). Furthermore, CMC is shown to be intimately related to the FKG inequality. Furthermore, a combinatorical application of CMC is given for which we do not know of another method to derive its result. Finally, we study the problem of the complexity of the computation of the CMC, which is a non-convex optimization problem with local maximas. We give a simple but exponential-time algorithm that is guaranteed to output the exact value of the generalized CMC.

cs.IT↗
arXiv2016

Information Theoretic cutting of a cake

Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e. one agent may like chocolate while the other may like cream). A fair division of the cake is one that takes into account the individual valuations of agents and partitions the cake based on some fairness criterion. Fair division may be accomplished in a distributed or centralized way. Due to its natural and practical appeal, it has been a subject of study in economics. To best of our knowledge the role of partial information in fair division has not been studied so far from an information theoretic perspective. In this paper we study two important algorithms in fair division, namely "divide and choose" and "adjusted winner" for the case of two agents. We quantify the benefit of negotiation in the divide and choose algorithm, and its use in tricking the adjusted winner algorithm. Also we analyze the role of implicit information transmission through actions for the repeated divide and choose problem by finding a trembling hand perfect equilibrium for an specific setup. Lastly we consider a centralized algorithm for maximizing the overall welfare of the agents under the Nash collective utility function (CUF). This corresponds to a clustering problem of the type traditionally studied in data mining and machine learning. Drawing a conceptual link between this problem and the portfolio selection problem in stock markets, we prove an upper bound on the increase of the Nash CUF for a clustering refinement.

cs.IT↗
arXiv2015

Perfectly Secure Index Coding

In this paper, we investigate the index coding problem in the presence of an eavesdropper. Messages are to be sent from one transmitter to a number of legitimate receivers who have side information about the messages, and share a set of secret keys with the transmitter. We assume perfect secrecy, meaning that the eavesdropper should not be able to retrieve any information about the message set. We study the minimum key lengths for zero-error and perfectly secure index coding problem. On one hand, this problem is a generalization of the index coding problem (and thus a difficult one). On the other hand, it is a generalization of the Shannon's cipher system. We show that a generalization of Shannon's one-time pad strategy is optimal up to a multiplicative constant, meaning that it obtains the entire boundary of the cone formed by looking at the secure rate region from the origin. Finally, we consider relaxation of the perfect secrecy and zero-error constraints to weak secrecy and asymptotically vanishing probability of error, and provide a secure version of the result, obtained by Langberg and Effros, on the equivalence of zero-error and $ε$-error regions in the conventional index coding problem.

cs.IT↗
arXiv2015

High Probability Guarantees in Repeated Games: Theory and Applications in Information Theory

We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high probability counterpart of the classical result of Mertens and Zamir for the zero-sum repeated games. Any payoff that can be guaranteed with high probability can be guaranteed in expectation, but the reverse is not true. Hence, unlike the average payoff case where the payoff guaranteed by each player is the negative of the payoff by the other player, the two guaranteed payoffs would differ in the high probability framework. One motivation for this framework comes from information transmission systems, where it is customary to formulate problems in terms of asymptotically vanishing probability of error. An application of our results to a class of compound arbitrarily varying channels is given.

cs.GT↗
arXiv2015

On ISI-free Modulations for Diffusion based Molecular Communication

A diffusion molecular channel is a channel with memory, as molecules released into the medium hit the receptors after a random delay. Coding over the diffusion channel is performed by choosing the type, intensity, or the released time of molecules diffused in the environment over time. To avoid intersymbol interference (ISI), molecules of the same type should be released at time instances that are sufficiently far apart. This ensures that molecules of a previous transmission are faded in the environment, before molecules of the same type are reused for signaling. In this paper, we consider ISI-free time-slotted modulation schemes. The maximum reliable transmission rate for these modulations is given by the constrained coding capacity of the graph that represents the permissible transmission sequences. However, achieving the constrained coding capacity requires long blocklengths and delays at the decoder, making it impractical for simple nanomachines. The main contribution of this paper is to consider modulations with small delay (short blocklength) and show that they get very close to constrained coding capacity.

cs.IT↗
arXiv2015

Zero Error Coordination

In this paper, we consider a zero error coordination problem wherein the nodes of a network exchange messages to be able to perfectly coordinate their actions with the individual observations of each other. While previous works on coordination commonly assume an asymptotically vanishing error, we assume exact, zero error coordination. Furthermore, unlike previous works that employ the empirical or strong notions of coordination, we define and use a notion of set coordination. This notion of coordination bears similarities with the empirical notion of coordination. We observe that set coordination, in its special case of two nodes with a one-way communication link is equivalent with the "Hide and Seek" source coding problem of McEliece and Posner. The Hide and Seek problem has known intimate connections with graph entropy, rate distortion theory, Renyi mutual information and even error exponents. Other special cases of the set coordination problem relate to Witsenhausen's zero error rate and the distributed computation problem. These connections motivate a better understanding of set coordination, its connections with empirical coordination, and its study in more general setups. This paper takes a first step in this direction by proving new results for two node networks.

cs.IT↗
arXiv2014

Deterministic Randomness Extraction from Generalized and Distributed Santha-Vazirani Sources

A Santha-Vazirani (SV) source is a sequence of random bits where the conditional distribution of each bit, given the previous bits, can be partially controlled by an adversary. Santha and Vazirani show that deterministic randomness extraction from these sources is impossible. In this paper, we study the generalization of SV sources for non-binary sequences. We show that unlike the binary case, deterministic randomness extraction in the generalized case is sometimes possible. We present a necessary condition and a sufficient condition for the possibility of deterministic randomness extraction. These two conditions coincide in "non-degenerate" cases. Next, we turn to a distributed setting. In this setting the SV source consists of a random sequence of pairs $(a_1, b_1), (a_2, b_2), \ldots$ distributed between two parties, where the first party receives $a_i$'s and the second one receives $b_i$'s. The goal of the two parties is to extract common randomness without communication. Using the notion of maximal correlation, we prove a necessary condition and a sufficient condition for the possibility of common randomness extraction from these sources. Based on these two conditions, the problem of common randomness extraction essentially reduces to the problem of randomness extraction from (non-distributed) SV sources. This result generalizes results of Gács and Körner, and Witsenhausen about common randomness extraction from i.i.d. sources to adversarial sources.

cs.CC↗
arXiv2014

Adaptive Molecule Transmission Rate for Diffusion Based Molecular Communication

In this paper, a simple memory limited transmitter for molecular communication is proposed, in which information is encoded in the diffusion rate of the molecules. Taking advantage of memory, the proposed transmitter reduces the ISI problem by properly adjusting its diffusion rate. The error probability of the proposed scheme is derived and the result is compared with the lower bound on error probability of the optimum transmitter. It is shown that the performance of introduced transmitter is near optimal (under certain simplifications). Simplicity is the key feature of the presented communication system: the transmitter follows a simple rule, the receiver is a simple threshold decoder and only one type of molecule is used to convey the information.

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