arXiv subjects

Hideki Yagi

Publications and source records attributed to Hideki Yagi.

At least 19 recordsLinked to original sources

arXiv2024

Optimum Achievable Rates in Two Random Number Generation Problems with $f$-Divergences Using Smooth R\'enyi Entropy

Two typical fixed-length random number generation problems in information theory are considered for general sources. One is the source resolvability problem and the other is the intrinsic randomness problem. In each of these problems, the optimum achievable rate with respect to the given approximation measure is one of our main concerns and has been characterized using two different information quantities: the information spectrum and the smooth R\'enyi entropy. Recently, optimum achievable rates with respect to $f$-divergences have been characterized using the information spectrum quantity. The $f$-divergence is a general non-negative measure between two probability distributions on the basis of a convex function $f$. The class of f-divergences includes several important measures such as the variational distance, the KL divergence, the Hellinger distance and so on. Hence, it is meaningful to consider the random number generation problems with respect to $f$-divergences. However, optimum achievable rates with respect to $f$-divergences using the smooth R\'enyi entropy have not been clarified yet in both of two problems. In this paper we try to analyze the optimum achievable rates using the smooth R\'enyi entropy and to extend the class of $f$-divergence. To do so, we first derive general formulas of the first-order optimum achievable rates with respect to $f$-divergences in both problems under the same conditions as imposed by previous studies. Next, we relax the conditions on $f$-divergence and generalize the obtained general formulas. Then, we particularize our general formulas to several specified functions $f$. As a result, we reveal that it is easy to derive optimum achievable rates for several important measures from our general formulas. Furthermore, a kind of duality between the resolvability and the intrinsic randomness is revealed in terms of the smooth R\'enyi entropy.

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arXiv2023

Outer Bounds on the CEO Problem with Privacy Constraints

We investigate the rate-distortion-leakage region of the Chief Executive Officer (CEO) problem, considering the presence of a passive eavesdropper and privacy constraints. We start by examining the region where a general distortion measure quantifies the distortion. While the inner bound of the region is derived from previous work, this paper newly develops an outer bound. To derive the outer bound, we introduce a new lemma tailored for analyzing privacy constraints. Next, as a specific instance of the general distortion measure, we demonstrate that the tight bound for discrete and Gaussian sources is obtained when the eavesdropper has no side information, and the distortion is quantified by the log-loss distortion measure. We further investigate the rate-distortion-leakage region for a scenario where the eavesdropper has side information, and the distortion is quantified by the log-loss distortion measure and provide an outer bound for this case. The derived outer bound differs from the inner bound by only a minor quantity that appears in the constraints associated with the privacy-leakage rates, and these bounds match when the distortion is large.

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arXiv2022

Secret-Key Agreement Using Physical Identifiers for Degraded and Less Noisy Authentication Channels

Secret-key agreement based on biometric or physical identifiers is a promising security protocol for authenticating users or devices with small chips due to its lightweight security. In previous studies, the fundamental limits of such a protocol were analyzed, and the results showed that two auxiliary random variables were involved in the capacity region expressions. However, with these two auxiliary random variables, the complexity of computing the capacity regions may be prohibitively high. To deal with this problem, we explore classes of authentication channels that require only one auxiliary random variable in the expressions of the capacity regions. It is revealed that for the classes of degraded and less noisy authentication channels, a single auxiliary random variable is sufficient to express the capacity regions. As specific examples, we derive the closed-form expressions for binary and Gaussian sources. Also, numerical calculations for Gaussian sources are provided to show the trade-off between secret-key and privacy-leakage rates under a given storage rate, and to illustrate how the noise in the enrollment phase affects the capacity region.

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arXiv2022

Secret Key-based Authentication With Passive Eavesdropper for Scalar Gaussian Sources

We analyze the fundamental trade-off of secret key-based authentication systems in the presence of an eavesdropper for correlated Gaussian sources. A complete characterization of trade-off among secret-key, storage, and privacy-leakage rates of both generated and chosen secret models is provided. One of the main contributions is revealing that unlike the known results for discrete sources, there is no need for the second auxiliary random variable in characterizing the capacity regions for the Gaussian cases. In addition, it is shown that the strong secrecy for secrecy-leakage of the systems can be achieved by an information-spectrum approach, and the parametric expressions (computable forms) of the capacity regions are also derived.

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arXiv2022

Biometric Identification Systems With Both Chosen and Generated Secret Keys by Allowing Correlation

We propose a biometric identification system where the chosen- and generated-secret keys are used simultaneously, and investigate its fundamental limits from information-theoretic perspectives. The system consists of two phases: enrollment and identification phases. In the enrollment phase, for each user, the encoder uses a secret key, which is chosen independently, and the biometric identifier to generate another secret key and a helper {data}. In the identification phase, observing the biometric sequence of the identified user, the decoder estimates index, chosen- and generated-secret keys of the identified user based on the helper {data} stored in the system database. In this study, the capacity region of such a system is characterized. In the problem setting, we allow chosen- and generated-secret keys to be correlated. As a result, by permitting the correlation of the two secret keys, the sum rate of the identification, chosen- and {generated-secret key} rates can achieve a larger value compared to the case where the keys {do not correlate}. Moreover, the minimum amount of the storage rate changes in accordance with both the identification and chosen-secret key rates, but that of the privacy-leakage rate depends only on the identification rate.

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arXiv2022

Unified Expression of Utility-Privacy Trade-off in Privacy-Constrained Source Coding

Privacy-constrained source coding problems have become increasingly important recently, and the utility-privacy trade-off has been investigated for various systems. As pioneering work, Yamamoto (1983) found theoretical limits of the coding rate, privacy and utility in two cases; (i) both public and private information is encoded and (ii) only public information is encoded. However, the theoretical limit has not been characterized in a more general case; (iii) encoded messages consist of public information and a part of private information. Then in this paper, we characterize the trade-off relation in case (iii) using rate-distortion theory. The obtained expression of the achievable region is a "unified expression" because it includes the ones in cases (i) and (ii) as special cases. The numerical results also demonstrate that neither case (i) nor (ii) are the best cases, and it is important to select the encoded information adequately in case (iii).

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arXiv2022

Identification, Secrecy, Template, and Privacy-Leakage of Biometric Identification System Under Noisy Enrollment

In this study, we investigate fundamental trade-off among identification, secrecy, template, and privacy-leakage rates in biometric identification systems. Ignatenko and Willems (2015) studied this system assuming that the channel in the enrollment process of the system is noiseless and they did not consider the template rate. In the enrollment process, however, it is highly considered that noise occurs when bio-data is scanned. In this paper, we impose a noisy channel in the enrollment process and characterize the capacity region of the rate tuples. The capacity region is proved by a novel technique via two auxiliary random variables, which has never been seen in previous studies. As special cases, the obtained result shows that the characterization reduces to the one given by Ignatenko and Willems (2015) where the enrollment channel is noiseless and there is no constraint on the template rate, and it also coincides with the result derived by Günlü and Kramer (2018) where there is only one individual.

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arXiv2020

Fundamental Limits of Biometric Identification Systems with Strong Secrecy

The fundamental limits of biometric identification systems under a strong secrecy criterion are investigated. In the previous studies of this scenario, the fundamental trade-off among secrecy, template, privacy- and secrecy-leakages has been revealed in the case where there is only one user, while the case of multiple users has not been discussed yet. In this study, we consider the system with exponentially many users, and we characterize the capacity region of the rate tuples including the user (identification) rate under the strong secrecy criterion. In the achievability proof, we derive a new method to incorporate multiple users by extending the random binning for one user's case. The obtained result shows that the characterization of the capacity region does not vary regardless of the weak or strong secrecy criterion in terms of secrecy-leakage.

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arXiv2020

Biometric Identification Systems With Noisy Enrollment for Gaussian Source

In the present paper, we investigate the fundamental trade-off of identification, secrecy, storage, and privacy-leakage rates in biometric identification systems for hidden or remote Gaussian sources. We introduce a technique for deriving the capacity region of these rates by converting the system to one where the data flow is in one-way direction. Also, we provide numerical calculations of three different examples for the generated-secret model. The numerical results imply that it seems hard to achieve both high secrecy and small privacy-leakage rates simultaneously. In addition, as special cases, the characterization coincides with several known results in previous studies.

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arXiv2020

Fundamental Limits of Identification System With Secret Binding Under Noisy Enrollment

We study the fundamental limits of biometric identification systems with chosen secret from an information theoretic perspective. Ignatenko and Willems (2015) characterized the capacity region of identification, secrecy, and privacy-leakage rates of the system provided that the enrollment channel is noiseless. In the enrollment process, however, it is highly considered that noise occurs when bio-data is scanned. Recently, Yachongka and Yagi (2019) characterized the capacity region of the system with generated secret considering noisy enrollment and template constraint. In this paper, we are interested in characterizing the capacity region of identification, secrecy, template, and privacy-leakage rates of the system with chosen secret under the same settings as Yachongka and Yagi (2019). As special cases, the obtained result shows that the characterization reduces to the one given by Ignatenko and Willems (2015) where the enrollment channel is noiseless and there is no constraint on the template rate, and it also coincides with the result derived by Günlü and Kramer (2018) where there is only one individual.

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arXiv2018

Variable-Length Lossy Compression Allowing Positive Overflow and Excess Distortion Probabilities

This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal rate are established by a new quantity based on the smooth max entropy (the smooth Rényi entropy of order zero). To derive the achievability bounds, we give an explicit code construction based on a distortion ball instead of using the random coding argument. The basic idea of the code construction is similar to the optimal code construction in the variable-length lossless source coding. Our achievability bounds are slightly different, depending on whether the encoder is stochastic or deterministic. One-shot results yield a general formula of the optimal rate for blocklength $n$. In addition, our general formula is applied to asymptotic analysis for a stationary memoryless source. As a result, we derive a single-letter characterization of the optimal rate by using the rate-distortion and rate-dispersion functions.

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arXiv2018

Optimum Overflow Thresholds in Variable-Length Source Coding Allowing Non-Vanishing Error Probability

The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem the optimum mean codeword length of variable-length codes has already been determined. On the other hand, in this paper, we focus on the overflow (or excess codeword length) probability instead of the mean codeword length. The infimum of overflow thresholds under the constraint that both of the error probability and the overflow probability are smaller than or equal to some constant is called the optimum overflow threshold. In this paper, we first derive finite-length upper and lower bounds on these probabilities so as to analyze the optimum overflow thresholds. Then, by using these bounds we determine the general formula of the optimum overflow thresholds in both of the first-order and second-order forms. Next, we consider another expression of the derived general formula so as to reveal the relationship with the optimum coding rate in the fixed-length source coding problem. We also derive general formulas of the optimum overflow thresholds in the optimistic coding scenario. Finally, we apply general formulas derived in this paper to the case of stationary memoryless sources.

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arXiv2018

Variable-Length Resolvability for Mixed Sources and its Application to Variable-Length Source Coding

In the problem of variable-length $δ$-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated distributions should be within a given constant $δ$ asymptotically. In this paper, we assume that the given channel input is a mixed source whose components may be general sources. To analyze the minimum achievable length rate of the uniform random number, called the $δ$-resolvability, we introduce a variant problem of the variable-length $δ$-channel resolvability. A general formula for the $δ$-resolvability in this variant problem is established for a general channel. When the channel is an identity mapping, it is shown that the $δ$-resolvability in the original and variant problems coincide. This relation leads to a direct derivation of a single-letter formula for the $δ$-resolvability when the given source is a mixed memoryless source. We extend the result to the second-order case. As a byproduct, we obtain the first-order and second-order formulas for fixed-to-variable length source coding allowing error probability up to $δ$.

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arXiv2017

Variable-Length Resolvability for General Sources and Channels

We introduce the problem of variable-length source resolvability, where a given target probability distribution is approximated by encoding a variable-length uniform random number, and the asymptotically minimum average length rate of the uniform random numbers, called the (variable-length) resolvability, is investigated. We first analyze the variable-length resolvability with the variational distance as an approximation measure. Next, we investigate the case under the divergence as an approximation measure. When the asymptotically exact approximation is required, it is shown that the resolvability under the two kinds of approximation measures coincides. We then extend the analysis to the case of channel resolvability, where the target distribution is the output distribution via a general channel due to the fixed general source as an input. The obtained characterization of the channel resolvability is fully general in the sense that when the channel is just the identity mapping, the characterization reduces to the general formula for the source resolvability. We also analyze the second-order variable-length resolvability.

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arXiv2017

Channel Resolvability Theorems for General Sources and Channels

In the problem of channel resolvability, where a given output probability distribution via a channel is approximated by transforming the uniform random numbers, characterizing the asymptotically minimum rate of the size of the random numbers, called the channel resolvability, has been open. This paper derives formulas for the channel resolvability for a given general source and channel pair. We also investigate the channel resolvability in an optimistic sense. It is demonstrated that the derived general formulas recapture a single-letter formula for the stationary memoryless source and channel. When the channel is the identity mapping, the established formulas reduce to an alternative form of the spectral sup-entropy rates, which play a key role in information spectrum methods. The analysis is also extended to the second-order channel resolvability.

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arXiv2016

Variable-Length Coding with Cost Allowing Non-Vanishing Error Probability

We derive a general formula of the minimum achievable rate for fixed-to-variable length coding with a regular cost function by allowing the error probability up to a constant $\varepsilon$. For a fixed-to-variable length code, we call the set of source sequences that can be decoded without error the dominant set of source sequences. For any two regular cost functions, it is revealed that the dominant set of source sequences for a code attaining the minimum achievable rate with a cost function is also the dominant set for a code attaining the minimum achievable rate with the other cost function. We also give a general formula of the second-order minimum achievable rate.

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arXiv2016

First- and Second-Order Coding Theorems for Mixed Memoryless Channels with General Mixture

This paper investigates the first- and second-order maximum achievable rates of codes with/without cost constraints for mixed {channels} whose channel law is characterized by a general mixture of (at most) uncountably many stationary and memoryless discrete channels. These channels are referred to as {mixed memoryless channels with general mixture} and include the class of mixed memoryless channels of finitely or countably memoryless channels as a special case. For mixed memoryless channels with general mixture, the first-order coding theorem which gives a formula for the $\varepsilon$-capacity is established, and then a direct part of the second-order coding theorem is provided. A subclass of mixed memoryless channels whose component channels can be ordered according to their capacity is introduced, and the first- and second-order coding theorems are established. It is shown that the established formulas reduce to several known formulas for restricted scenarios.

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arXiv2014

Single-Letter Characterization of Epsilon-Capacity for Mixed Memoryless Channels

For the class of mixed channels decomposed into stationary memoryless channels, single-letter characterizations of the $\varepsilon$-capacity have not been known except for restricted classes of channels such as the regular decomposable channel introduced by Winkelbauer. This paper gives single-letter characterizations of $\varepsilon$-capacity for mixed channels decomposed into at most countably many memoryless channels with a finite input alphabet and a general output alphabet with/without cost constraints. It is shown that a given characterization reduces to the one for the channel capacity given by Ahlswede when $\varepsilon$ is zero. In the proof of the coding theorem, the meta converse bound, originally given by Polyanskiy, Poor and Verdú, is particularized for the mixed channel decomposed into general component channels.

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