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.

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.

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 where the side-information does not exist, we demonstrate that our tight exponent of the Wyner-Ahlswede-Körner (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 and Effros and further developed by Tyagi and Watanabe. A key component of the methodology by Tyagi and Watanabe is the use of soft Markov constraint, which was originally introduced by Oohama, as a penalty term to prove the Markov constraint at the end. A technical innovation of this paper compared to Tyagi and Watanabe is recognizing that the soft Markov constraint is a part of the exponent, rather than a penalty term that should vanish at the end; this recognition enables us to derive the matching achievability bound. In fact, via numerical experiment, we provide evidence that the soft Markov constraint is strictly positive. Compared to Oohama’s derivation of the lower bound, which relies on the single-letterization of a certain moment-generating function, the derivation of our tight exponent only involves manipulations of the Kullback-Leibrer divergence and Shannon entropies. 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 the strong converse exponent to the privacy amplification.

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.

In message authentication, we consider a situation where a sender sends messages to a receiver through an insecure channel. In the insecure channel, there is a risk of impersonation or substitution by an adversary. Message authentication is a scheme to detect such attacks and to accept legitimate messages as legitimate. In Igawa's study, the upper and lower bounds of the product of the success probabilities of the attacks are derived under the condition that each party observes correlated i.i.d. sequences as secret information, and it is shown that the upper and lower bounds are asymptotically equal in certain conditions. In Shikata's study, the success probabilities of attacks are evaluated in terms of the Rényi entropy in the situation where the sender and receiver share a secret key of finite length. In this study, we evaluate the success probability of attacks using the conditional Rényi entropy for the case where each party observes correlated information of finite length and the sender and receiver observe the same, which is one of the open questions in Igawa's study. We can also think of such a situation as one where the secret key is partially leaked. First, we extend the definitions of the attack success probabilities to our situation. Next, we evaluate these probabilities using the conditional Rényi entropy by dividing them into cases by the size of the alphabet of the secret key.

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. The achievability part is derived by a careful analysis of the type argument. 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.

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.

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.

The achievable rate region of Wyner-Ahlswede-Körner coding problem for mixed sources is investigated. Wyner-Ahlswede-Körner coding problem consists of two encoders and one decoder for two correlated sources. We derive the singleletter formula for mixed sources from Miyake and Kanaya’s general result. It clarifies the behaviour of the Wyner-Ahlswede-Körner achievable region for non-ergodic sources; depending on the property of side-information, the achievable regions are different.

The isomorphism problem in the ergodic theory is revisited from the perspective of information spectrum approach, an approach that has been developed to investigate coding problems for non-ergodic random processes in information theory. It is proved that the information spectrum is invariant under isomorphisms. This result together with an analysis of information spectrum provide a conceptually simple proof of the result by Sujan, which claims that the entropy spectrum is invariant under isomorphisms. It is also discussed under what circumstances the same information spectrum implies the existence of an isomorphism.

The task of manipulating correlated random variables in a distributed setting has received attention in the fields of both Information Theory and Computer Science. Often shared correlations can be converted, using a little amount of communication, into perfectly shared uniform random variables. Such perfect shared randomness, in turn, enables the solutions of many tasks. Even the reverse conversion of perfectly shared uniform randomness into variables with a desired form of correlation turns out to be insightful and technically useful. In this article, we describe progress-to-date on such problems and lay out pertinent measures, achievability results, limits of performance, and point to new directions.

We present an information theoretic proof of the nonsignalling multiprover parallel repetition theorem, a recent extension of its two-prover variant that underlies many hardness of approximation results. The original proofs used de Finetti type decomposition for strategies. We present a new proof that is based on a technique we introduced recently for proving strong converse results in multiuser information theory and entails a change of measure after replacing hard information constraints with soft ones.

The problem of exactly generating a general random process (target process) by using another general random process (coin process) is studied. The performance of the interval algorithm, introduced by Han and Hoshi, is analyzed from a perspective of information spectral approach. When either the coin process or the target process has one point spectrum, asymptotic optimality of the interval algorithm among any random number generation algorithms is proved, which demonstrates utility of the interval algorithm beyond the ergodic process. The feasibility condition of exact random number generation is also elucidated.

The strong converse for a coding theorem shows that the optimal asymptotic rate possible with vanishing error cannot be improved by allowing a fixed error. Building on a method introduced by Gu and Effros for centralized coding problems, we develop a general and simple recipe for proving strong converse that is applicable for distributed problems as well. Heuristically, our proof of strong converse mimics the standard steps for proving a weak converse, except that we apply those steps to a modified distribution obtained by conditioning the original distribution on the event that no error occurs. A key component of our recipe is the replacement of the hard Markov constraints implied by the distributed nature of the problem with a soft information cost using a variational formula introduced by Oohama. We illustrate our method by providing a short proof of the strong converse for the Wyner-Ziv problem and strong converse theorems for interactive function computation, common randomness and secret key agreement, and the wiretap channel; the latter three strong converse problems were open prior to this work.

In the distributed function computation problem, dichotomy theorems, initiated by Han-Kobayashi, seek to classify functions by whether the rate regions for function computation improve on the Slepian-Wolf regions or not. In this paper, we develop a general approach to derive converse bounds on the distributed function computation problem. By using this approach, we derive an improved sufficient condition on the dichotomy theorem in the multiterminal distributed computing for the class of i.i.d. sources with positivity condition.

We consider the hypothesis testing in which the null hypothesis is simple but the alternative hypothesis is composite. By using the information geometry method, we propose a test based on relative direction of the alternative hypothesis from the null hypothesis in the exponential coordinate of probability simplex. Pareto optimality of the proposed test is proved in the second-order regime. In contrast to the exponential error trade-off regime, there is no test that universally attains the same second-order exponent as the optimal likelihood ratio test.

Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We propose a new interactive protocol for data exchange, which increases the communication size in steps until the task is done. We also derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Our single-shot analysis applies to all discrete random variables and yields upper and lower bounds of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general source sequence, such as a mixture of independent and identically distributed (IID) random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.

Multiple parties observe correlated data generated independently and identically (in time) from a known joint distribution. Parties communicate with each other interactively to enable each party to recover the data observed by all the other parties and attain omniscience. We characterize the asymptotic growth of the number of bits of interactive communication required by the parties to attain omniscience up to the second-order term. For the converse, we provide a single-shot lower bound for the required number of bits of communication, which yields the asymptotic result as a special case. It is shown that the knowledge of the distribution can be used to modify the recently proposed recursive data exchange protocol to render it optimal up to the second-order term. As a corollary, we provide a precise characterization of the reduction in communication for omniscience due to interaction.

The problem of zero-rate multiterminal hypothesis testing is revisited from the perspective of information-spectrum approach and finite blocklength analysis. A Neyman-Pearson-like test is proposed and its non-asymptotic performance is clarified, for a short block length, it is numerically determined that the proposed test is superior to the previously reported Hoeffding-like test proposed by Han-Kobayashi. For a large deviation regime, it is shown that our proposed test achieves an optimal trade-off between the type I and type II exponents presented by Han-Kobayashi. Among the class of symmetric (type-based) testing schemes, when the type I error probability is non-vanishing, the proposed test is optimal up to the second-order term of the type II error exponent; the latter term is characterized in terms of the variance of the projected relative entropy density. The information geometry method plays an important role in the analysis as well as the construction of the test.

We show a reduction method to construct a code for the Gray-Wyner (GW) network from a given code for the Wyner-Ahlswede-Korner (WAK) network. By combining this reduction with a converse bound on the GW network, we derive a converse bound on the WAK network. The derived bound gives an alternative proof of the strong converse theorem for the WAK network.

Two parties observing correlated random variables seek to run an interactive communication protocol. How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical distance of the joint distribution of the input and the transcript of the original protocol? We present an information spectrum approach for this problem whereby the information complexity of the protocol is replaced by its information complexity density. Our single-shot bounds relate the communication complexity of simulating a protocol to tail bounds for information complexity density. As a consequence, we obtain a strong converse and characterize the second-order asymptotic term in communication complexity for independent and identically distributed observation sequences. Furthermore, we obtain a general formula for the rate of communication complexity, which applies to any sequence of observations and protocols. Connections with results from theoretical computer science and implications for the function computation problem are discussed.

Multiple parties observing correlated data seek to recover each other's data and attain omniscience. To that end, they communicate interactively over a noiseless broadcast channel - each bit transmitted over this channel is received by all the parties. We give a universal interactive communication protocol, termed the recursive data exchange protocol (RDE), which attains omniscience for any sequence of data observed by the parties and provide an individual sequence guarantee of performance. As a by-product, for observations of length n, we show the universal rate optimality of RDE up to an O(n-1/2√log n) term in a generative setting where the data sequence is independent and identically distributed (in time). Furthermore, drawing on the duality between omniscience and secret key agreement due to Csiszár and Narayan, we obtain a universal protocol for generating a multiparty secret key of rate at most O(n-1/2√log n) less than the maximum rate possible. A key feature of RDE is its recursive structure whereby when a subset A of parties recover each-other's data, the rates appear as if the parties have been executing the protocol in an alternative model where the parties in A are collocated.

The coding problem over the Gray-Wyner network is studied from the second-order coding rates perspective. A tilted information density for this network is introduced in the spirit of Kostina-Verdú, and, under a certain regularity condition, the second-order region is characterized in terms of the variance of this tilted information density and the tangent vector of the first-order region. The second-order region is proved by the type method: the achievability part is proved by the type-covering argument, and the converse part is proved by a refinement of the perturbation approach that was used by Gu-Effros to show the strong converse of the Gray-Wyner network. This is the first instance that the second-order region is characterized for a multi-terminal problem, where the characterization of the first-order region involves an auxiliary random variable.

A simulation of an interactive protocol entails the use of interactive communication to produce the output of the protocol to within a fixed statistical distance ε. Recent works have proposed that the information complexity of the protocol plays a central role in characterizing the minimum number of bits that the parties must exchange for a successful simulation, namely the distributional communication complexity of simulating the protocol. Several simulation protocols have been proposed with communication complexity depending on the information complexity of the simulated protocol. However, in the absence of any general lower bounds for distributional communication complexity, the conjectured central role of information complexity is far from settled. We fill this gap and show that the distributional communication complexity of ε-simulating a protocol is bounded below by the ε-tail λε of the information complexity density, a random variable with information complexity as its expected value. For protocols with bounded number of rounds, we give a simulation protocol that yields a matching upper bound. Thus, it is not information complexity but λε that governs the distributional communication complexity.

Multiple parties observing correlated data seek to recover each other's data and attain omniscience. To that end, they communicate interactively over a noiseless broadcast channel: Each bit transmitted over this channel is received by all the parties. We give a universal interactive protocol for omniscience which requires communication of rate only O(n-1/2√log n) more than the optimal rate for every independent and identically distributed (in time) sequence of data.

The problem of distributed function computation for the class of smooth sources is studied, where functions to be computed are compositions of symbol-wise functions and some outer functions that are not symbol-wise. The optimal rate for computing those functions is characterized in terms of the Slepian-Wolf rate and an equivalence class of sources induced by functions. To prove the result, a new method to derive a converse bound for distributed computing is proposed; the bound is derived by identifying a source that is inevitably conveyed to the decoder and by explicitly constructing a code for reproducing that source. As a byproduct, it provides a conceptually simple proof of the known fact that computing a Boolean function may require as large rate as reproducing the entire source.

We revisit the problem of secret key agreement using interactive public communication for two parties and propose a new secret key agreement protocol. The protocol attains the secret key capacity for general observations and attains the second-order asymptotic term in the maximum length of a secret key for independent and identically distributed observations. In contrast to the previously suggested secret key agreement protocols, the proposed protocol uses interactive communication. In fact, the standard one-way communication protocol used prior to this paper fails to attain the asymptotic results above. Our converse proofs rely on a recently established upper bound for secret key lengths. Both our lower and upper bounds are derived in a single-shot setup and the asymptotic results are obtained as corollaries.

In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on the block length. We also characterize the asymptotic behaviors of the large deviation regime and the moderate deviation regime by using our bounds, which implies that our bounds are asymptotically tight in those regimes. We also show the second-order rates of those problems, and derive single letter forms of the variances characterizing the second-order rates. Furthermore, we address the relative entropy rate and the modified mutual information rate for these problems.

Coded source compression, also known as source compression with helpers, has been a major variant of distributed source compression, but has hitherto received little attention in the quantum regime. This letter treats and solves the corresponding quantum coded source compression through an observation that connects coded source compression with channel simulation. First, we consider classical source coding with quantum side information, where the quantum side information is observed by a helper and sent to the decoder via a classical channel. We derive a single-letter characterization of the achievable rate region for this problem. The direct coding theorem of our result is proved via the measurement compression theory of Winter, a quantum-to-classical channel simulation. Our result reveals that a helper's scheme which separately conducts a measurement and a compression is suboptimal, and measurement compression seems necessary to achieve the optimal rate region. We then study coded source compression in the fully quantum regime, where two different scenarios are considered depending on the types of communication channels between the legitimate source and the receiver. We further allow entanglement assistance from the quantum helper in both scenarios. We characterize the involved quantum resources and derive single-letter expressions of the achievable rate region. The direct coding proofs are based on well-known quantum protocols, the quantum state merging protocol, and the fully quantum Slepian-Wolf protocol, together with the quantum reverse Shannon theorem.

We study classical source coding with quantum side-information where the quantum side-information is observed by a helper and sent to the decoder via a classical channel. We derive a single-letter characterization of the achievable rate region for this problem. The direct part of our result is proved via the measurement compression theory by Winter. Our result reveals that a helper's scheme that separately conducts a measurement and a compression is suboptimal, and the measurement compression is fundamentally needed to achieve the optimal rate region.

The problem of distributed data compression for function computation is considered, where (i) the function to be computed is not necessarily symbol-wise function and (ii) the information source has memory and may not be stationary nor ergodic. We introduce the class of smooth sources and give a sufficient condition on functions so that the achievable rate region for computing coincides with the Slepian-Wolf region (i.e., the rate region for reproducing the entire source) for any smooth sources. Moreover, for symbol-wise functions, the necessary and sufficient condition for the coincidence is established. Our result for the full side-information case is a generalization of the result by Ahlswede and Csiszár; our dichotomy theorem is different from Han and Kobayashi's dichotomy theorem, which reveals an effect of memory in distributed function computation. All results are given not only for fixed-length coding but also for variable-length coding in a unified manner.

We revisit A.C. Yao's classic problem of secure function computation by interactive communication, in an information theoretic setting. Our approach, based on examining the underlying common randomness, provides a new proof of the characterization of a securely computable function by deterministic protocols. This approach also yields a characterization of the minimum communication needed for secure computability.

Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Furthermore, we propose an interactive protocol for data exchange which increases the communication size in steps until the task is done and matches the performance of our lower bound. Our single-shot analysis applies to all discrete random variables and yields upper and lower bound of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general sequence such as mixture of IID random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for the IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.

We derive impossibility (converse) bounds for the efficiency of implementing information theoretically secure oblivious transfer and bit commitment using correlated observations. Our approach is based on relating these problems to that of testing if the observations of the parties are conditionally independent given the adversary's observation. The resulting bounds strengthen and improve upon several previously known results.

This paper studies variable-length (VL) source coding of general sources with side-information. Novel one-shot coding bounds for Slepian-Wolf (SW) coding, which give nonasymptotic tradeoff between the error probability and the codeword length of VL-SW coding, are established. One-shot results are applied to asymptotic analysis, and a general formula for the optimal coding rate achievable by weakly lossless VL-SW coding (i.e., VL-SW coding with vanishing error probability) is derived. Our general formula reveals how the encoder side-information and/or VL coding improve the optimal coding rate in the general setting. In addition, it is shown that if the encoder side-information is useless in weakly lossless VL coding then it is also useless even in the case where the error probability may be positive asymptotically.

We consider information theoretic secret key (SK) agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the SK length, which is derived using a reduction of binary hypothesis testing to multiparty SK agreement. Building on this basic result, we derive new converses for multiparty SK agreement. Furthermore, we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to SK agreement. Finally, we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data, using an interactive public communication that by itself does not give away the value of the function. In many cases, we strengthen and improve upon previously known converse bounds. Our results are single-shot and use only the given joint distribution of the correlated observations. For the case when the correlated observations consist of independent and identically distributed (in time) sequences, we derive strong versions of previously known converses.

We present a novel nonasymptotic or finite blocklength achievability bounds for three side-information problems in network information theory. These include: 1) the Wyner-Ahlswede-Körner (WAK) problem of almost-lossless source coding with rate-limited side-information; 2) the Wyner-Ziv (WZ) problem of lossy source coding with side-information at the decoder; and 3) the Gel'fand-Pinsker (GP) problem of channel coding with noncausal state information available at the encoder. The bounds are proved using ideas from channel simulation and channel resolvability. Our bounds for all three problems improve on all previous nonasymptotic bounds on the error probability of the WAK, WZ, and GP problems-in particular those derived by Verdú. Using our novel nonasymptotic bounds, we recover the general formulas for the optimal rates of these side-information problems. Finally, we also present achievable second-order coding rates by applying the multidimensional Berry-Esséen theorem to our new nonasymptotic bounds. Numerical results show that the second-order coding rates obtained using our nonasymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds.

In coding schemes for the wire-tap channel or for broadcast channels with confidential messages, it is well-known that the sender needs to use stochastic encoding to avoid information about the transmitted confidential message from being leaked to an eavesdropper. In this paper, we investigate the tradeoff between the rate of random numbers needed to realize the stochastic encoding and the rates of common, private, and confidential messages. For the direct theorem, we use the superposition coding scheme for the wire-tap channel, recently proposed by Chia and El Gamal, and its strong security is proved. The matching converse theorem is also established. Our result clarifies that a combination of ordinary stochastic encoding and channel prefixing by channel simulation is suboptimal.

We revisit the problem of secret key agreement using interactive public communication for two parties. When the underlying observations are independent and identically distributed, we establish the second-order asymptotic term in the maximum length of a secret key. Furthermore, for general observations, we establish the secret key capacity. Underlying our proofs is a new secret key agreement scheme and a recently established upper bound on secret key lengths.

We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then, we show that the sample mean of the generator of the exponential family is an asymptotically efficient estimator. Further, we also define a curved exponential family of transition matrices. Using a transition matrix version of the Pythagorean theorem, we give an asymptotically efficient estimator for a curved exponential family.

In this paper, we investigate weak variable-length Slepian-Wolf (VL-SW) coding of general sources. First, by using the information-spectrum method, we show novel non-asymptotic trade-off between the error probability and the codeword length of VL-SW coding. Then, we give an asymptotic formula for the optimal coding rate achievable by VL-SW coding. Especially, we investigate VL-SW coding for mixed sources. Our results spotlights the fact that distinguishability between component sources plays an important role in adjusting the coding rate at the encoder. We also demonstrate that our general results derive a known formula for the optimal achievable rate of VL-SW coding for mixture of i.i.d. sources and extend to countably infinite alphabet case with mild condition.

We study the (almost lossless) joint source-channel coding problem from the moderate deviations perspective where the bandwidth expansion ratio tends towards the ratio of the channel capacity and source entropy at a rate larger than n−1/2(n being the channel blocklength) and the error probability decays subexponentially. We consider the stationary ergodic Markov (SEM) source as well as discrete memoryless and additive SEM channels. We also discuss the loss due to separation in the moderate deviations setting.

We study the problem of channel resolvability for fixed i.i.d. input distributions and discrete memoryless channels (DMCs), and derive the strong converse theorem for any DMCs that are not necessarily full rank. We also derive the optimal second-order rate under a condition. Furthermore, under the condition that a DMC has the unique capacity achieving input distribution, we derive the optimal second-order rate of channel resolvability for the worst input distribution.

We investigate the Wyner-Ziv coding in which the statistics of the principal source is known but the statistics of the channel generating the side information is unknown except that it is in a certain class. The class consists of channels such that the distortion between the principal source and side information is smaller than a threshold, but channels may be neither stationary nor ergodic. In this situation, we define a new rate-distortion function as the minimum rate such that there exists a Wyner-Ziv code that is universal for every channel in the class. Then, we show an upper bound and a lower bound on the rate-distortion function, and derive a matching condition such that the upper and lower bounds coincide. The relation between the new rate-distortion function and rate-distortion function of the Heegard-Berger problem is also discussed.

The cognitive interference channel with confidential messages (CICC) proposed by Lianget al.is investigated. When the security is considered in coding systems, it is well-known that the sender needs to use a stochastic encoding to avoid the information about the transmitted confidential message to be leaked to an eavesdropper. For the CICC, the tradeoff between the rate of the random number to realize the stochastic encoding and the communication rates is investigated, and the optimal tradeoff is completely characterized.

This paper investigates the privacy amplification problem, and compares the existing two bounds: the exponential bound derived by one of the authors and the min-entropy bound derived by Renner. It turns out that the exponential bound is better than the min-entropy bound when a security parameter is rather small for a block length, and that the min-entropy bound is better than the exponential bound when a security parameter is rather large for a block length. Furthermore, we present another bound that interpolates the exponential bound and the min-entropy bound by a hybrid use of the Rényi entropy and the inf-spectral entropy.

We investigate the Wyner-Ziv coding in which the statistics of the principal source is known but the statistics of the channel generating the side-information is unknown except that it is in a certain class. The class consists of channels such that the distortion between the principal source and the side-information is smaller than a threshold, but channels may be neither stationary nor ergodic. In this situation, we define a new rate-distortion function as the minimum rate such that there exists a Wyner-Ziv code that is universal for every channel in the class. Then, we show an upper bound and a lower bound on the rate-distortion function, and derive a matching condition such that the upper and lower bounds coincide.

We present a novel achievability bound for the Wyner-Ahlswede-Körner (WAK) problem of lossless source coding with rate-limited side-information. This bound is proved using ideas from channel simulation and channel resolvability. The bound improves on all previous non-asymptotic bounds on the error probability of the WAK problem. We also present achievable second-order coding rates by applying the multidimensional Berry-Essèen theorem to our new non-asymptotic bound.

In coding schemes for the wire-tap channel or the broadcast channels with confidential messages, it is well known that the sender needs to use a stochastic encoding to avoid the information about the transmitted confidential message to be leaked to an eavesdropper. In this paper, it is investigated that the trade-off between the rate of the random number to realize the stochastic encoding and the rates of the common, private, and confidential messages. For the direct theorem, the superposition coding scheme for the wire-tap channel recently proposed by Chia and El Gamal is employed, and its strong security is proved. The matching converse theorem is also established. Our result clarifies that a combination of the ordinary stochastic encoding and the channel prefixing by the channel simulation is suboptimal.

We investigate the privacy amplification problem in which Eve can observe the uniform binary source through a binary erasure channel (BEC) or a binary symmetric channel (BSC). For this problem, we derive the so-called expurgation exponent of the information leaked to Eve. The exponent is derived by relating the leaked information to the error probability of the linear code that is generated by the linear hash function used in the privacy amplification, which is also interesting in its own right. The derived exponent is larger than state-of-the-art exponent recently derived by Hayashi at low rate.

In this paper, we consider a situation such that legitimate parties, Alice and Bob, share an identical source to generate a secret key, and an eavesdropper, Eve, can access a correlated data that is stored in a storage with bounded size. Then, Alice and Bob want to extract a secret as long as possible. We show a privacy amplification theorem for this problem, i.e., we clarify the rate of key generation for given rate of Eve's storage. The problem can be regarded as a dual randomness generation problem of the Wyner-Ahlswede-Körner type source coding system, and the techniques used in the proof are exchanged, i.e., the so-called Markov lemma is used in the converse part, and the so-called image size characterization is used in the direct part.

This paper investigates a lossy source coding problem in which two decoders can access their side-information respectively. The correlated sources are a product of two component correlated sources, and we exclusively investigate the case such that each component is degraded. We show the rate-distortion function for that case, and give the following observations. When the components are degraded in matched order, the rate distortion function of the product sources is equal to the sum of the component-wise rate distortion functions. On the otherhand, the former is strictly smaller than the latter when the component sources are degraded in mismatched order.

We investigate the secret key agreement from correlated vector Gaussian sources in which legitimate parties can use public communication with limited rate. For the class of protocols with one-way public communication, we show that the optimal trade-off between the rate of key generation and the rate of the public communication is characterized as an optimization problem of a Gaussian random variable. The characterization is derived by using the enhancement technique introduced by Weingarten for multiple-input-multiple-output (MIMO) Gaussian broadcast channel.

We investigate the secret key agreement from correlated vector Gaussian sources in which the legitimate parties can use the public communication with limited rate. For the class of protocols with the one-way public communication, we show that the optimal trade-off between the rate of key generation and the rate of the public communication is characterized as an optimization problem of a Gaussian random variable. The characterization is derived by using the enhancement technique introduced by Weingarten et. al. for MIMO Gaussian broadcast channel.

The axis compensation is a procedure in which the sender and the receiver compensate the axes of their transmitter and detector so that the bit sequence can be transmitted more reliably. We show the optimal axis compensations maximizing the key generation rate. We consider the case in which only the receiver is allowed to compensate his axis, and the case in which both the sender and the receiver are allowed to compensate their axes. For unital channels, we clarify that the optimal key generation rates for both cases coincide if they utilize the mismatched measurement outcomes in the channel estimation. We also clarify that the optimal key generation rates for both cases do not coincide in general if they do not utilize the mismatched measurement outcomes in the channel estimation.

The privacy amplification is a technique to distill a secret key from a random variable by a hash function so that the distilled key and an eavesdropper's random variable is statistically independent. There are two kinds of security criteria for the key distilled by the privacy amplification: the weak security criterion and the strong security criterion. As a technique to distill a secret key, it is known that the encoder of a Slepian-Wolf (the source coding with full side-information at the decoder) code can be used as a hash function for the privacy amplification if we employ the weak security criterion. In this paper, we show that the encoder of a Slepian-Wolf code cannot be used as a hash function for the privacy amplification if we employ the strong security criterion.

This paper deals with a universal coding problem for a certain kind of multiterminal source coding network called a generalized complementary delivery network. In this network, messages from multiple correlated sources are jointly encoded, and each decoder has access to some of the messages to enable it to reproduce the other messages. Both fixed-to-fixed length and fixed-to-variable length lossless coding schemes are considered. Explicit constructions of universal codes and the bounds of the error probabilities are clarified by using methods of types and graph-theoretical analysis.

We consider the problem of secret key agreement in Gaussian Maurer’s Model. In Gaussian Maurer’s model, legitimate receivers, Alice and Bob, and a wire-tapper, Eve, receive signals randomly generated by a satellite through three independent memoryless Gaussian channels respectively. Then Alice and Bob generate a common secret key from their received signals. In this model, we propose a protocol for generating a common secret key by using the result of soft-decision of Alice and Bob’s received signals. Then, we calculate a lower bound on the secret key rate in our proposed protocol. As a result of comparison with the protocol that only uses hard-decision, we found that the higher rate is obtained by using our protocol.

We propose an information reconciliation protocol that uses two-way classical communication. In the case of the BB84 protocol and the six-state protocol, the key rates of the quantum key distribution (QKD) protocols that use our proposed information reconciliation protocol are higher than previously known protocols for wide range of error rates. We also clarify the relation between the proposed protocol and known QKD protocols and entanglement distillation protocols (EDPs).

This paper shows that the BB84 protocol with random privacy amplification is secure with a higher key rate than Mayers' estimate with the same error rate. Consequently, the tolerable error rate of this protocol is increased from 7.5% to 11%. We also extend this method to the case of estimating error rates separately in each basis, which enables us to securely share a longer key.