We reinvestigate the general distributed secure source coding based on the common key cryptosystem proposed by Oohama and Santoso (ITW 2021). They proposed a framework of distributed source encryption and derived the necessary and sufficient conditions to have reliable and secure transmission. However, the bounds of the rate region, which specifies both necessary and sufficient conditions to have reliable and secure transmission under the proposed cryptosystem, were derived based on a self-tailored non-standard security criterion. In this paper we adopt the standard security criterion, i.e., standard mutual information. We successfully establish the bounds of the rate region based on this security criterion. Information spectrum method and a variant of Birkhoff-von Neumann theorem play important roles in deriving our result.

We study the universal coding problem for the general framework of source encryption with a symmetric key under the side-channel attacks, which is posed and investigated by Oohama and Santoso (2022). The reliable and secure rate region indicating the trade off between the compression rate of the ciphertext and the rate constraint imposed on the adversary for secure source transmission was established by Oohama and Santoso (2022). In this paper we focus on our attention to strengthening the direct coding theorem. We prove the existence of encryption/decryption schemes, which are universal in the sense that they work effectively for any distributions of the plain text, any noisy channels through which the adversary observe the corrupted version of the key, and any measurement device used for collecting the physical information. Those schemes have a good performance such that if we compress the ciphertext with rate within the reliable and secure rate region, then: (1) anyone with secret key will be able to decrypt and decode the ciphertext correctly, but (2) any adversary who obtains the ciphertext and also the side physical information will not be able to obtain any information about the hidden source as long as the leaked physical information is encoded with a rate within the rate constraint.

In this paper we consider the separate coding problem for$L+1$correlated Gaussian memoryless sources. We deal with the case where$L$separately encoded data of sources work as side information at the decoder for the reconstruction of the remaining source. In this paper we study the case where$L+1$sources satisfy a kind of tree structure on their correlation. This tree structure of information sources is called the TS condition. In his previous work the author determine the sum rate part of the rate distortion region for the case where information sources satisfy the TS condition. In this paper we derive an explicit recursive formula of this sum rate part. This result completes the author's previous work in which the formula is established for some limited case.

We are interested in investigating the security of source encryption with a symmetric key under side-channel attacks. In this paper, we propose a general framework of source encryption with a symmetric key under the side-channel attacks, which applies to any source encryption with a symmetric key and any kind of side-channel attacks targeting the secret key. We also propose a new security criterion for strong secrecy under side-channel attacks, which is a natural extension of mutual information, i.e., the maximum conditional mutual information between the plaintext and the ciphertext given the adversarial key leakage, where the maximum is taken over all possible plaintext distribution. Under this new criterion, we successfully formulate the rate region, which serves as both necessary and sufficient conditions to have secure transmission even under side-channel attacks. Furthermore, we also prove another theoretical result on our new security criterion, which might be interesting in its own right: in the case of the discrete memoryless source, no perfect secrecy under side-channel attacks in the standard security criterion, i.e., the ordinary mutual information, is achievable without achieving perfect secrecy in this new security criterion, although our new security criterion is more strict than the standard security criterion.

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 the 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.

We pose and investigate the distributed secure source coding based on the common key cryptosystem. This cryptosystem includes the secrecy amplification problem for distributed encrypted sources with correlated keys using post-encryption-compression, which was previously studied by Santoso and Oohama. In this paper we propose another new security criterion which is generally more strict compared with the commonly used security criterion based on the upper-bound of mutual information between the plaintext and the ciphertext. Under this criterion, we establish the necessary and sufficient condition for the secure transmission of correlated sources.

We consider the coding problem for the state dependent channel with full state information at the sender and partial state information at the receiver. For this state dependent channel, the channel capacity under rate constraint on the state information at the decoder was determined by Steinberg. In this paper we prove the strong converse theorem for the problem. To prove this theorem, we use a new method, which is a coupling of information spectrum method with the change of measure method introduced by Tyagi and Watanabe.

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.

Dueck and Körner's reliability function for discrete memoryless channels for rates above the capacity coincides with Arimoto's exponent of correct decoding probability. The two exponent functions are described by seemingly different optimization problems over the space of probability distributions. Arimoto gave an iterative algorithm for solving the optimization problem that appears in his exponent function. However, no algorithm to solve the optimization problem that appears in Dueck and Körner's exponent has been proposed. This paper proposes a new iterative algorithm for solving the minimization problem in Dueck and Körner's exponent. In the proposed algorithm, a double minimization form with respect to two joint distributions on input and output symbols is introduced. This double minimization is connected to another double minimization that appears in Arimoto's algorithm. Such a connection leads to a quadruple minimization problem, by which the match of Arimoto and Dueck-Körner exponents is easily proved.

In this paper we provide a new inequality useful for the proofs of strong converse theorems in the network information theory. We apply this inequality to the recent work by Tyagi and Watanabe on the strong converse theorem for the Wyner-Ziv source coding problem to obtain a new strong converse outer bound. This outer bound deviates from the Wyner-Ziv rate distortion region with the order of O(1/√n) on the length n of source outputs.

We consider the secure communication problem of broadcasting of two encrypted sources against an adversary which launches side-channel attacks. The adversary is not only allowed to eavesdrop the ciphertexts in the public communication channel but is also allowed to obtain the side information on the secret keys via the side-channel. In this paper, we propose a theoretical framework to solve this problem and also propose a countermeasure based on the post-encryption-compression paradigm. We provide an explicit sufficient condition to attain the exponential decay of the information leakage as the block lengths of encrypted sources become large.

We study the determination problem of the channel capacity for the discrete memoryless channels in the finite blocklength regime. We derive explicit lower and upper bounds of the capacity. We shall demonstrate that the information spectrum approach is quite useful for investigating this problem.

In this paper, we are interested in the problem of strengthening the secrecy of distributed encryption in a particular case where the encryption keys are correlated to each other. We show that the post-encryption-compression (PEC) paradigm provides a suitable solution for the problem without requiring any additional secret randomness. More precisely, we show that in the case of one-time-pad encryption, we can use affine encoders with specific properties to strengthen the secrecy by using them to compress the ciphertexts before sending them to public communication channels. We show how to derive those affine encoders using universal code construction paradigm. The universal code construction gives us advantages as follows. 1) We can construct good encoders based on the transmission rates only, without knowing the value of the distribution of sources or keys. 2) Reliability and secrecy are achievable by construction even in particular cases such as follows: 1) only the range of correlation between keys is known but the exact amount is unknown or 2) the correlation between keys are changing time to time within a certain range. We also derive explicit lower bounds on the achievable reliability and secrecy exponents, i.e., the exponential rates of decay of the probability of decoding error and of the information leakage as the block length becomes large.

We study side-channel attacks for the Shannon cipher system. To pose side channel-attacks to the Shannon cipher system, we regard them as a signal estimation via encoded data from two distributed sensors. This can be formulated as the one helper source coding problem posed and investigated by Ahlswede, Korner(1975), and Wyner(1975). We further investigate the posed problem to derive new secrecy bounds. Our results are derived by a coupling of the result Watanabe and Oohama(2012) obtained on bounded storage eavesdropper with the exponential strong converse theorem Oohama(2015) established for the one helper source coding problem.

In this paper, we propose the application of post-encryption-compression (PEC) to strengthen the secrecy in the case of distributed encryption where the encryption keys are correlated to each other, without additional randomness. We show that, in the case of one-time-pad encryption, certain affine encoders are sufficient for strengthening the secrecy by using them to compress the ciphertexts before sending them to public communication channels. We show how to explicitly construct those affine encoders using universal code construction paradigm. The universal code construction gives us advantages as follows. (1) We can construct good encoders based on the transmission rates only, without knowing the value of the distribution of sources or keys. (2) Reliability and secrecy are achievable by construction even in cases such as follows: (1) only the range of correlation between keys is known but the exact amount is unknown, or (2) the correlation between keys are changing time to time within a certain range.We also derive concrete lower bounds on the achievable reliability and secrecy exponents, i.e., the exponential rates of decay of the probability of decoding error and of the information leakage as the block length n becomes large.

We consider the additive white Gaussian noise channels. We prove that the error probability of decoding tends to one exponentially for rates above the capacity and derive the optimal exponent function. We shall demonstrate that the information spectrum approach is quite useful for investigating this problem.

In this paper, we consider a system where multiple sources are encrypted in separated nodes and sent through their respective public communication channels into a joint sink node. We are interested at the problem on protecting the security of an already existing system such above, which is found out to have correlated encryption keys. In particular, we focus on finding a solution without introducing additional secret keys and with minimal modification to minimize the cost and the risk of bringing down an already running system. We propose a solution under a security model where an eavesdropper obtains all ciphertexts, i.e., encrypted sources, by accessing available public communication channels. Our main technique is to use encoders of certain linear codes to encode the ciphertexts before sending them to public communication channels. We show that if the rates of linear codes are within a certain rate region: (1) the success probability of any eavesdropper to extract the original sources from the encoded ciphertexts without the keys is negligible, while (2) one who has legitimate keys is able to retrieve the original source data with negligible error probability.

The form of Dueck and Körner's exponent function for correct decoding probability for discrete memoryless channels at rates above the capacity is similar to the form of Csiszár and Körner's exponent function for correct decoding probability in lossy source coding for discrete memoryless sources at rates below the rate distortion function. We recently gave a new algorithm for computing Dueck and Körner's exponent. In this paper, we give an algorithm for computing Csiszár and Körner's exponent. The proposed algorithm can also be used to compute cutoff rate and the rate distortion function.

We consider the state dependent channels with full state information with at the sender and partial state information at the receiver. For this state dependent channel, the channel capacity under rate constraint on the state information at the decoder was determined by Steinberg. In this paper, we study the correct probability of decoding at rates above the capacity. We prove that when the transmission rate is above the capacity this probability goes to zero exponentially and derive an explicit lower bound of this exponent function.

We consider the discrete memoryless degraded broadcast channels. We prove that the error probability of decoding tends to one exponentially for rates outside the capacity region and derive an explicit lower bound of this exponent function. We shall demonstrate that the information spectrum approach is quite useful for investigating this problem.

We consider the one helper source coding problem posed and investigated by Ahlswede, Körner and Wyner. In this system, the error probability of decoding goes to one as the source block length n goes to infinity. This implies that we have a strong converse theorem for the one helper source coding problem. In this paper we provide the much stronger version of this strong converse theorem for the one helper source coding problem. We prove that the error probability of decoding tends to one exponentially and derive an explicit lower bound of this exponent function.

We consider the discrete memoryless degraded broadcast channels with feedback. We prove that the error probability of decoding tends to one exponentially for rates outside the capacity region and derive an explicit lower bound of this exponent function. We shall demonstrate that the information spectrum approach is quite useful for investigating this problem.

For a discrete memoryless channel, a lower bound for the correct decoding probability exponent was derived by Arimoto. He also gave an iterative algorithm for computing the exponent. Subsequently, Dueck and Körner determined the optimal exponent function of the correct decoding probability. In this paper, a new iterative algorithm that computes Dueck and Körner's exponent is presented.

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 consider the one helper source coding problem posed and investigated by Ahlswede, Körner, and Wyner for a class of information sources with memory. For this class of information sources we give explicit inner and outer bounds of the admissible rate region. We also give one nontrivial example for the inner and outer bounds to match.

We consider the distributed source coding system of L correlated Gaussian sources Yl, l = 1, 2, ... , L, which are noisy observations of correlated Gaussian remote sources Xk, k = 1,2, ..., K. We assume that YL= t(Y1, Y2,...,YL) is an observation of the source vector XK= t(X1, X2, . . . , XK), having the form YL= AXK+NL, where A is a L×K matrix and NL= t(N1, N2, ... , NL) is a vector of L-independent Gaussian random variables also independent of XK. In this system, L correlated Gaussian observations are separately compressed by L encoders and sent to the information processing center. We study the remote source coding problem, where the decoder at the center attempts to reconstruct the remote source XK. We consider three distortion criteria based on the covariance matrix of the estimation error on XK. For each of those three criteria, we derive explicit inner and outer bounds of the rate distortion region. Next, in the case of K = L and A = IL, we study the multiterminal source coding problem, where the decoder wishes to reconstruct the observation YL= XL+ NL. To investigate this problem, we shall establish a result that provides a strong connection between the remote source coding problem and multiterminal source coding problem. Using this result, we derive several new partial solutions to the multiterminal source coding problem.

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.

In this paper we consider the identification (ID) via multiple access channels (MACs). In the general MAC the ID capacity region includes the ordinary transmission (TR) capacity region. In this paper we discuss the converse coding theorem. We estimate two types of error probabilities of identification for rates outside capacity region, deriving some function which serves as a lower bound of the sum of two error probabilities of identification. This function has a property that it tends to zero as n → ∞ for noisy channels satisfying the strong converse property. Using this property, we establish that the transmission capacity region is equal to the ID capacity for the MAC satisfying the strong converse property. To derive the result we introduce a new resolvability problem on the output from the MAC. We further develop a new method of converting the direct coding theorem for the above MAC resolvability problem into the converse coding theorem for the ID via MACs.

In identification via channels, the sum of two types of error probabilities of identification goes to one as the block length of transmission tends to infinity at rates above capacity when channels satisfy some stochastic properties. This is well known as a strong converse theorem for the identification via channels. In this paper, we prove that the sum of two error probabilities tends to one exponentially and derive an explicit lower bound of this exponent function.

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.

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.

We consider the distributed source coding system for$L$correlated memoryless Gaussian remote sources specified with$L$correlated Gaussian random variables$X_{i}$,$i=1,2,\ldots,L$. We deal with the case where each of$L$distributed encoders cannot directly observe the source$X_{i}$but its noisy version$Y_{i}=X_{i}+N_{i}$. Here,$N_{i}$,$i=1,2,\ldots, L$are independent additive$L$Gaussian noises also independent of$X_{i}$,$i=1,2,\ldots, L$. On this coding system, the determination problem of the rate distortion region remains open in general. In this paper, we derive explicit outer and inner bounds of the rate distortion region. We further find an explicit sufficient condition for those two bounds to match. We also study the sum rate part of the rate distortion region when the correlation has some symmetrical property. We derive an explicit upper bound of the sum rate part from the inner bounds of the rate distortion region. On a lower bound, we derive a new explicit bound by making full use of the symmetrical property of the correlation. We further derive an explicit necessary and sufficient condition for the lower bound to coincide with the upper bound.

We consider the distributed source coding system of L correlated Gaussian sources Yi, i = 1, 2, ..., L. We assume that YL=t(Y1, Y2, ..., YL) is an observation of the remote source vector XL=t(X1,X2, ..., XL), having the formYL= XK+ NL, where NL=t(N1,N2, ..., NL) is a vector of L independent Gaussian random variables also independent of XL. In this system L correlated Gaussian observations are separately compressed by Lencoders and sent to the information processing center. In this paper, we study the multiterminal source coding problem where the decoder wishes to reconstruct the observation YL= XL+ NL. In the previous work the author derived inner and outer bounds of the rate distortion region and derived a matching condition of the above two bounds. In this paper, based on this matching condition, we give a detail analysis on a part of the inner bound where it coincides with the outer bound. We further study an explicit characterization of the sum rate part of the rate distortion region when the observed Gaussian sources have a certain symmetric property.

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.

In this paper we analyze the interval algorithm for random number generation proposed by Han and Hoshi using the expression of real numbers on the interval$[0,1)$. We first establish an explicit representation of the interval algorithm with the representation of real numbers on the interval$[0,1)$based on number systems. Next, using the expression of the interval algorithm, we give a rigorous analysis of the interval algorithm. We discuss the difference between the expected number of the coin tosses in the interval algorithm and their upper bound derived by Han and Hoshi and show that it can be characterized explicitly with the established expression of the interval algorithm.

We consider a distributed source coding problem of L correlated Gaussian observations Yi, i = 1, 2, ..., L. We assume that the random vector YL=t(Y1, Y2, ..., YL) is an observation of the Gaussian random vector XK=t(X1,X2, ..., XK), having the form YL= AXK+ NL, where A is a L × K matrix and NL=t(N1, N2, ..., NL) is a vector of L independent Gaussian random variables also independent of XK. We consider two distortion criterion based on the covariance matrix of the estimation error on XK. One is the criterion called the vector distortion criterion distortion region where each of the the diagonal elements of the covariance matrix is upper bounded by a prescribed level. The other is the criterion called the sum distortion criterion where the trace of the covariance matrix is upper bounded by a prescribed level. For each of the above two distortion criterion we derive explicit inner and outer bounds of the rate distortion region. We also derive an explicit matching condition in the case of the sum distortion criterion.

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.

We consider the distributed source coding system of L correlated Gaussian sources Yi, i = 1,2, ⋯, L. We assume that YL=t(Y1, Y2, ⋯, YL) is an observation of the remote source vector XL=t(X1, X2, ⋯, XL), having the form YL= XK+ NL, where NL=t(N1, N2, ···, NL) is a vector of L independent Gaussian random variables also independent of XL. In this system L correlated Gaussian observations are separately compressed by L encoders and sent to the information processing center. In this paper, we study the multiterminal source coding problem where the decoder wishes to reconstruct the observation YL= XL+NL. We consider three distortion criteria based on the covariance matrix of the estimation error on YL. For each of those three criteria we derive explicit inner and outer bounds of the rate distortion region.

We consider the separate source coding problem of L correlated Gaussian observations Yi, i = 1, 2, …, L. We consider the case that Yi, i = 1, 2, …, L satisfy Yi= Xi+Ni, i = 1, 2, … , L where Xi, i = 1, 2, …, L are L correlated Gaussian random variables and Ni, i = 1, 2, … L are independent additive Gaussian noises also independent of Xi, i = 1, 2, …, L. On this coding system the determination problem of the rate distortion region remains open. In our previous works, we derived explicit outer and inner bounds of the rate distortion region and sufficient condition for the inner and outer bounds to match. In this paper we derive a stronger sufficient condition for those two bounds to match.

In this paper we consider the separate coding problem for L+1 correlated memoryless sources. We deal with the case where L sources work as partial side information at the decoder for the reconstruction of the remaining source. The determination problem of the rate-distortion region for this system is the so called many-help-one problem and has been known as a highly challenging problem for almost thirty years. We survey previous results on this problem. Through survey we discuss some implication of the many-help-one problem for the progress of multiterminal rate-distortion theory.

We consider a relay channel where a relay helps the transmission of messages from one sender to one receiver. The relay is considered not only as a sender that helps the message transmission but as a wire-tapper who can obtain some knowledge about the transmitted messages. In this paper we study the coding problem of the relay channel under the situation that some of transmitted messages are confidential to the relay. A security of such confidential messages is measured by the conditional entropy. The rate region is defined by the set of transmission rates for which messages are reliably transmitted and the security of confidential messages is larger than a prescribed level. In this paper we give two definition of the rate region. We first define the rate region in the case of deterministic encoder and call it the deterministic rate region. Next, we define the rate region in the case of stochastic encoder and call it the stochastic rate region. We derive explicit inner and outer bounds for the above two rate regions and present a class of relay channels where two bounds match. From the derived results, we can see that stochastic encoder can enlarge the rate region. We also evaluate the deterministic rate region of the Gaussian relay channel with confidential messages.

In this paper we consider the separate coding problem for L +1 correlated Gaussian memoryless sources. We deal with the case where L separately encoded data of sources work as side information at the decoder for the reconstruction of the remaining source. The determination problem of the rate distortion region for this system is the so called many-help-one problem and has been known as a highly challenging problem. The author determined the rate distortion region in the case where the L sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given. This condition on the correlation is called the CI condition. In this paper we extend the author's previous result to the case where L + 1 sources satisfy a kind of tree structure on their correlation. We call this tree structure of information sources the TS condition. This condition contains the CI condition as a special case. In this paper we derive an explicit outer bound of the rate distortion region when information sources satisfy the TS condition. Furthermore, we show that for L = 2 this outer bound coincides with the rate distortion region. We also present a sufficient condition for the outer bound to coincide with the rate distortion region

This paper deals with the random number generation problem in the framework of separate coding system for correlated memoryless sources. L-correlated data sequences with length n are separately encoded to nRi, i = 1,2,..., L, at each location and those are sent to the information processing center where the encoder wish to generate approximations of nRL+ibits uniformly distributed random sequence from L-received random messages. Admissible rate region are defined by the set of all the rate vector RL+1= (R1,...RL, RL+1) for which the approximation error goes to zero as n tends to infinity. In this paper, we examine asymptotic behaviors of the approximation error inside and outside the admissible rate region. We derive an explicit lower bound of the optimal exponent for the approximation error to vanish and show that it can be attained by the universal codes. Furthermore, we derive an explicit lower bound of the optimal exponent for the approximation error to tend to 2 as n goes to infinity outside the admissible rate region. From those results, we can know an explicit form of the admissible rate region

In this paper we analysis the interval algorithm for random number generation proposed by Han and Hoshi using the expression of real numbers on the interval [0,1). We first an explicit representation of the interval algorithm with the representation of real numbers on the interval [0,1) based one number systems. Next, using the expression of the interval algorithm, we give a rigorous analysis of the interval algorithm. We discuss the difference between the expected number of the coin tosses in the interval algorithm and their upper bound derived by Han and Hoshi and show that it can be characterized explicitly with the established expression of the interval algorithm.

In this paper, we consider the separate coding problem for L+1 correlated Gaussian memoryless sources. We deal with the case where L sources work as partial side information at the decoder for the reconstruction of the remaining source. The determination problem of the rate-distortion region for this system is the so-called many-help-one problem and it has been known as a highly challenging problem for almost 20 years. In this paper, we give a partial solution to this problem. We determine the rate-distortion region in the case where the L sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given. The additive white Gaussian noise CEO problem is a special case of this. We also discuss the relation of the result previous results of ours

In this paper we consider the identification (ID) via multiple access channels (MAC). Steinberg (1998) proved that in the general MAC the ID capacity region is equal to the ordinary transmission capacity region. In this paper we give an alternative proof for the converse coding theorem for the ID via MAC. We estimate two types of error probabilities of identification for rates outside the capacity region, deriving some function which serves as a lower bound of the sum of two error probabilities of identification. The result of Steinberg immediately follows from this result.

We consider a relay channel where a relay helps the transmission of messages from one sender to one receiver. The relay is considered not only as a sender that helps the message transmission but as a wire-tapper who can obtain some knowledge about the transmitted messages. In this paper we study the coding problem of the relay channel under the situation that some of transmitted messages are confidential to the relay. A security of such confidential messages is measured by the conditional entropy. We derive an explicit inner bound of the capacity region characterized with the set of transmission rates for which messages are reliably transmitted and the security of confidential messages is larger than a prescribed level.

A new multiterminal source coding problem called the CEO problem was presented and investigated by Berger, Zhang, and Viswanathan. Recently, Viswanathan and Berger have investigated an extension of the CEO problem to Gaussian sources and call it the quadratic Gaussian CEO problem. They considered this problem from a statistical viewpoint, deriving some interesting results. In this paper, we consider the quadratic Gaussian CEO problem from a standpoint of multiterminal rate-distortion theory. We regard the CEO problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given. This viewpoint leads us to a complete solution to the problem. We determine the tradeoff between the total amount of rate and squared distortion, deriving an explicit formula of the rate-distortion function. The derived function has the form of a sum of two nonnegative functions. One is a classical rate-distortion function for single Gaussian source and the other is a new rate-distortion function which dominates the performance of the system for a relatively small distortion. It follows immediately from our result that the conjecture of Viswanathan and Berger on the asymptotic behavior of minimum squared distortion for large rates is true.

In this paper, we consider the problem of separate coding for two correlated memoryless Gaussian sources. We determine the rate-distortion region in the special case when one source provides partial side information to the other source. We also show that the previously obtained inner region of the rate-distortion region is partially tight. A rigorous proof of the direct coding theorem is also given.

On the coding for correlated sources we extend the Slepian-Wolf (1973) data compression system (called the SW system) to define a new system (called the SWL system), where two separate encoders of the SW system are mutually linked. Determining the optimal error exponent for all rates inside the admissible rate region remains an open problem for the SW system. We completely solve this problem for the SWL system, and show that the optimal exponents can be achieved by universal codes. Furthermore, it is shown that the linkage of two encoders does not extend the admissible rate region and does not even improve the exponent of correct decoding outside this region. The zero error data transmission problem for the SWL system is also considered. We determine the zero error rate region, the admissible rate region under the condition that the decoding error probability is strictly zero, and show that this region can be attained by universal codes. Furthermore, we make it clear that the linkage of encoders enlarges the zero error rate region. It is interesting to note that the above results for the SWL system correspond in some sense to the previous results for the discrete memoryless channel with feedback.

Universal coding for the Slepian-Wolf (1973) data compression system is considered. We shall demonstrate based on a simple observation that the error exponent given by Csiszar and Korner (1980) for the universal coding system can strictly be sharpened in general for a region of relatively higher rates. This kind of observation can be carried over also to the case of lower rates outside the Slepian-Wolf region, which establishes the strong converse along with the optimal exponent.>