arXiv subjects

Shun Watanabe

Publications and source records attributed to Shun Watanabe.

At least 19 recordsLinked to original sources

arXiv2026

Distributed Hypothesis Testing Against Dependence

We study distributed hypothesis testing and establish the exact error exponent in single-letter form for new testing problems. In distributed hypothesis testing, a receiver decides between $\mathcal{H}_0:P_{XY}$ and $\mathcal{H}_1:Q_{XY}$ based on $Y^n$ and a rate-limited description of $X^n$. So far, such single-letter forms are known only for testing against independence, studied by Ahlswede and Csisz\'ar, and testing against conditional independence, studied by Rahman and Wagner. In this paper, we study testing against dependence, where $P_{XY}=P_XP_Y$, and show that its error exponent is given by Han's exponent, which is established by single-letterizing a multi-letter version of Han's exponent. Our result disproves a previous conjecture by Han claiming that the error exponent is given by the lautum information. We then consider the Cartesian product of testing against dependence and testing against independence, and derive a single-letter characterization of its error exponent. Finally, we study testing against conditional dependence, which is the dependence-testing counterpart of the setting studied by Rahman and Wagner. We derive a single-letter converse bound for the error exponent by introducing and solving a related setting where the side information is also available to the transmitter. We show that our converse bound is tight in some cases by using a conditional-coding version of the quantization scheme, which improves upon existing achievability schemes.

cs.IT↗

arXiv2026

On The Most Discriminative Boolean Functions for Correlated Sources

Motivated by a conjecture of Amari and Kobayashi, we study the problem of identifying pairs of Boolean functions that maximize the Kullback-Leibler divergence between two distributions obtained by separately compressing two correlated sources. When the reference distribution corresponds to independent sources, this problem reduces to the problem of maximizing mutual information, for which the optimality of dictator functions has been proved by Pichler, Piantanida, and Matz. For the problem of maximizing Fisher information, which can be viewed as a local version of the problem studied in this paper, Amari and Kobayashi conjectured that parity functions are optimal. For unbiased pairs of Boolean functions, and for identical pairs in the nonnegative correlation regime, we prove that both the divergence and the Fisher information are maximized by level-$k$ functions, namely, functions whose Fourier coefficients are supported only on level $k$. Since level-$k$ functions include parity functions, this gives a partial resolution of the conjecture of Amari and Kobayashi. Furthermore, in the framework of Bayesian distributed one-bit hypothesis testing, we prove that level-$k$ functions are optimal among all pairs of functions. Finally, we also discuss the one function version of the problem studied in this paper, which can be regarded as the divergence analogue of the Courtade and Kumar conjecture.

cs.IT↗

arXiv2026

The Condition for Structured Coding to Improve Random Coding in the Binary Modulo-sum Problem

The modulo-sum problem, proposed by K\"orner and Marton (KM), is a representative problem in the field of distributed source coding. In the modulo-sum problem, two correlated sources are encoded separately, and the decoder decodes the modulo-sum of the sources. It is clear that the Slepian-Wolf (SW) coding rate region is achievable for the modulo-sum problem. K\"orner and Marton proved that the SW coding rate region can be improved by structured coding based on linear codes. Ahlswede and Han (AH) proposed AH coding, which combines structured coding and random coding, and expressed its rate using auxiliary random variables. However, it was conjectured that the minimum sum rate of AH coding cannot be smaller than the minimum of the sum rates achievable by KM coding or SW coding. Subsequently, Kakishima and Watanabe considered a multi-letter extension of AH coding, and designed the auxiliary random variables by taking the XOR of adjacent bits of the source sequences. Through numerical computation, they demonstrated the existence of source parameters for which multi-letter AH coding improves upon SW coding. However, this confirmation remained numerical, and the conditions under which multi-letter extended AH coding improves upon SW coding have not been analytically characterized. In this study, we analytically characterize the conditions under which multi-letter extended AH coding improves upon SW coding. Our condition is tight in the sense that it coincides with the complement of the known SW optimal sufficient condition. To obtain the conditions, we apply the method of types to reduce the evaluation of the multi-letter expression to a comparison of single-letter divergences, which might be of independent interest.

cs.IT↗

arXiv2026

UMVUE-Type Estimators under Bregman Losses

We study unbiased estimation under Bregman losses and develop an extension of the classical theory of uniformly minimum variance unbiased estimators (UMVUEs). Exploiting bias--variance-type decompositions for Bregman divergences, we consider two natural loss functions, $D_{\varphi}(\theta,\hat{\theta})$ and $D_{\varphi}(\hat{\theta},\theta)$, and their corresponding notions of unbiasedness. We show that the latter formulation reduces to the classical setting, whereas the former yields a different framework in which unbiasedness is characterized in the dual space induced by $\nabla\varphi$. For the nontrivial case, we establish analogs of the Rao--Blackwell and Lehmann--Scheff{\'e} theorems, providing a systematic construction of type-I Bregman UMVUEs.

cs.IT↗

arXiv2026

Classical-Quantum Channel Resolvability Using Matrix Multiplicative Weight Update Algorithm

We study classical-quantum (C-Q) channel resolvability. C-Q channel resolvability has been proved by only random coding in the literature. In our previous study, we proved channel resolvability by deterministic coding, using multiplicative weight update algorithm. We extend this approach to C-Q channels and prove C-Q channel resolvability by deterministic coding, using the matrix multiplicative weight update algorithm. This is the first approach to C-Q channel resolvability using deterministic coding.

cs.IT↗

arXiv2025

Tight Exponential Strong Converses for Lossy Source Coding with Side-Information and Distributed Function Computation

The exponential strong converse for a coding problem states that, if a coding rate is beyond the theoretical limit, the correct probability converges to zero exponentially. For the lossy source coding with side-information, also known as the Wyner-Ziv (WZ) problem, a lower bound on the strong converse exponent was derived by Oohama. In this paper, we derive the tight strong converse exponent for the WZ problem; as a special case, we also derive the tight strong converse exponent for the distributed function computation problem. For the converse part, we use the change-of-measure argument developed in the literature and the soft Markov constraint introduced by Oohama; the matching achievability is proved via the Poisson matching approach recently introduced by Li and Anantharam. Our result is build upon the recently derived tight strong converse exponent for the Wyner-Ahlswede-Korner (WAK) problem; however, compared to the WAK problem, more sophisticated argument is needed. As an illustration of the necessity of the soft Markov constraint, we present an example such that the soft Markov constraint is strictly positive.

cs.IT↗

arXiv2025

Channel Resolvability Using Multiplicative Weight Update Algorithm

We study the channel resolvability problem, which is used to prove strong converse of identification via channel. Channel resolvability has been solved by only random coding in the literature. We prove channel resolvability using the multiplicative weight update algorithm. This is the first approach to channel resolvability using non-random coding.

cs.IT↗

arXiv2025

An Improved Lower Bound on Oblivious Transfer Capacity Using Polarization and Interaction

We consider the oblivious transfer (OT) capacities of noisy channels against the passive adversary; this problem has not been solved even for the binary symmetric channel (BSC). In the literature, the general construction of OT has been known only for generalized erasure channels (GECs); for the BSC, we convert the channel to the binary symmetric erasure channel (BSEC), which is a special instance of the GEC, via alphabet extension and erasure emulation. In a previous paper by the authors, we derived an improved lower bound on the OT capacity of BSC by proposing a method to recursively emulate BSEC via interactive communication. In this paper, we introduce two new ideas of OT construction: (i) via ``polarization" and interactive communication, we recursively emulate GECs that are not necessarily a BSEC; (ii) in addition to the GEC emulation part, we also utilize interactive communication in the key agreement part of OT protocol. By these methods, we derive lower bounds on the OT capacity of BSC that are superior to the previous one for a certain range of crossover probabilities of the BSC. Via our new lower bound, we show that, at the crossover probability being zero, the slope of tangent of the OT capacity is unbounded.

cs.IT↗

arXiv2024

Characterization of Exponential Families of Lumpable Stochastic Matrices

It is known that the set of lumpable Markov chains over a finite state space, with respect to a fixed lumping function, generally does not form an exponential family of stochastic matrices. In this work, we explore efficiently verifiable necessary and sufficient conditions for families of lumpable transition matrices to form exponential families. To this end, we develop a broadly applicable dimension-based method for determining whether a given family of stochastic matrices forms an exponential family.

math.PR↗

arXiv2024

An Improved Lower Bound on Oblivious Transfer Capacity via Interactive Erasure Emulation

We revisit the oblivious transfer (OT) capacities of noisy channels against the passive adversary, which have been identified only for a limited class of channels. In the literature, the general construction of oblivious transfer has been known only for generalized erasure channels (GECs); for other channels, we first convert a given channel to a GEC via alphabet extension and erasure emulation, and then apply the general construction for GEC. In this paper, we derive an improved lower bound on the OT capacity of the binary symmetric channel (BSC) and binary symmetric erasure channel (BSEC) by proposing a new protocol; by using interactive communication between the sender and the receiver, our protocol emulates erasure events recursively in multiple rounds. We also discuss a potential necessity of multiple rounds interactive communication to attain the OT capacity.

cs.IT↗

arXiv2023

Geometric Aspects of Data-Processing of Markov Chains

We examine data-processing of Markov chains through the lens of information geometry. We first establish a theory of congruent Markov morphisms within the framework of stochastic matrices. Specifically, we introduce and justify the concept of a linear right inverse (congruent embedding) for lumping, a well-known operation used in Markov chains to extract coarse information. Furthermore, we inspect information projections onto geodesically convex sets of stochastic matrices, and show that under some conditions, projecting (m-projection) onto doubly convex submanifolds can be regarded as a form of data-processing. Finally, we show that the family of lumpable stochastic matrices can be meaningfully endowed with the structure of a foliated manifold and motivate our construction in the context of embedded models and inference.

math.PR↗

arXiv2023

A Geometric Reduction Approach for Identity Testing of Reversible Markov Chains

We consider the problem of testing the identity of a reversible Markov chain against a reference from a single trajectory of observations. Employing the recently introduced notion of a lumping-congruent Markov embedding, we show that, at least in a mildly restricted setting, testing identity to a reversible chain reduces to testing to a symmetric chain over a larger state space and recover state-of-the-art sample complexity for the problem.

math.PR↗

arXiv2022

Tight Exponential Strong Converse for Source Coding Problem with Encoded Side Information

The source coding problem with encoded side information is considered. A lower bound on the strong converse exponent has been derived by Oohama, but its tightness has not been clarified. In this paper, we derive a tight strong converse exponent. For the special case such that the side-information does not exists, we demonstrate that our tight exponent of the WAK problem reduces to the known tight expression of that special case while Oohama's lower bound is strictly loose. The converse part is proved by a judicious use of the change-of-measure argument, which was introduced by Gu-Effros and further developed by Tyagi-Watanabe. Interestingly, the soft Markov constraint, which was introduced by Oohama as a proof technique, is naturally incorporated into the characterization of the exponent. A technical innovation of this paper is recognizing that the soft Markov constraint is a part of the exponent, rather than a penalty term that should be vanished. In fact, via numerical experiment, we provide evidence that the soft Markov constraint is strictly positive. The achievability part is derived by a careful analysis of the type argument; however, unlike the conventional analysis for the achievable rate region, we need to derive the soft Markov constraint in the analysis of the correct probability. Furthermore, we present an application of our derivation of strong converse exponent to the privacy amplification.

cs.IT↗

arXiv2022

Universal and Efficient p-Doping of Organic Semiconductors by Electrophilic Attack of Cations

Doping is of great importance to tailor the electrical properties of semiconductors. However, the present doping methodologies for organic semiconductors (OSCs) are either inefficient or can only apply to a small number of OSCs, seriously limiting their general application. Herein, we reveal a novel p-doping mechanism by investigating the interactions between the dopant trityl cation and poly(3-hexylthiophene) (P3HT). It is found that electrophilic attack of the trityl cations on thiophenes results in the formation of alkylated ions that induce electron transfer from neighboring P3HT chains, resulting in p-doping. This unique p-doping mechanism can be employed to dope various OSCs including those with high ionization energy (IE=5.8 eV). Moreover, this doping mechanism endows trityl cation with strong doping ability, leading to polaron yielding efficiency of 100 % and doping efficiency of over 80 % in P3HT. The discovery and elucidation of this novel doping mechanism not only points out that strong electrophiles are a class of efficient p-dopants for OSCs, but also provides new opportunities towards highly efficient doping of OSCs.

cond-mat.mtrl-sci↗

arXiv2022

On Sub-optimality of Random Binning for Distributed Hypothesis Testing

We investigate the quantize and binning scheme, known as the Shimokawa-Han-Amari (SHA) scheme, for the distributed hypothesis testing. We develop tools to evaluate the critical rate attainable by the SHA scheme. For a product of binary symmetric double sources, we present a sequential scheme that improves upon the SHA scheme.

cs.IT↗

arXiv2021

Information Geometry of Reversible Markov Chains

We analyze the information geometric structure of time reversibility for parametric families of irreducible transition kernels of Markov chains. We define and characterize reversible exponential families of Markov kernels, and show that irreducible and reversible Markov kernels form both a mixture family and, perhaps surprisingly, an exponential family in the set of all stochastic kernels. We propose a parametrization of the entire manifold of reversible kernels, and inspect reversible geodesics. We define information projections onto the reversible manifold, and derive closed-form expressions for the e-projection and m-projection, along with Pythagorean identities with respect to information divergence, leading to some new notion of reversiblization of Markov kernels. We show the family of edge measures pertaining to irreducible and reversible kernels also forms an exponential family among distributions over pairs. We further explore geometric properties of the reversible family, by comparing them with other remarkable families of stochastic matrices. Finally, we show that reversible kernels are, in a sense we define, the minimal exponential family generated by the m-family of symmetric kernels, and the smallest mixture family that comprises the e-family of memoryless kernels.

math.ST↗

arXiv2021

Minimax Converse for Identification via Channels

A minimax converse for the identification via channels is derived. By this converse, a general formula for the identification capacity, which coincides with the transmission capacity, is proved without the assumption of the strong converse property. Furthermore, the optimal second-order coding rate of the identification via channels is characterized when the type I error probability is non-vanishing and the type II error probability is vanishing. Our converse is built upon the so-called partial channel resolvability approach; however, the minimax argument enables us to circumvent a flaw reported in the literature.

cs.IT↗

arXiv2020

Two-dimensional hole gas in organic semiconductors

A highly conductive metallic gas that is quantum mechanically confined at a solid-state interface is an ideal platform to explore nontrivial electronic states that are otherwise inaccessible in bulk materials. Although two-dimensional electron gas (2DEG) has been realized in conventional semiconductor interfaces, examples of two-dimensional hole gas (2DHG), which is the counter analogue of 2DEG, are still limited. Here, we report the observation of a 2DHG in solution-processed organic semiconductors in conjunction with an electric double-layer using ionic liquids. A molecularly flat single crystal of high mobility organic semiconductors serves as a defect-free interface that facilitates two-dimensional confinement of high-density holes. Remarkably low sheet resistance of 6 k$Ω$ and high hole gas density of 10$^{14}$ cm$^{-2}$ result in a metal-insulator transition at ambient pressure. The measured degenerated holes in the organic semiconductors provide a broad opportunity to tailor low-dimensional electronic states using molecularly engineered heterointerfaces.

cond-mat.mtrl-sci↗