This paper deals with the random number generation problem under the framework of a separate coding system for correlated memoryless sources posed and investigated by Slepian and Wolf. Two correlated data sequences with length n are separately encoded to nR1, nR2 bit messages at each location and those are sent to the information processing center where the encoder wish to generate an approximation of the sequence of independent uniformly distributed random variables with length nR3 from two received random messages. The admissible rate region is defined by the set of all the triples (R1,R2,R3) for which the approximation error goes to zero as n tends to infinity. In this paper we examine the asymptotic behavior 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.

We investigate the secret key agreement from correlated 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 a closed form expression of the optimal trade-off between the rate of key generation and the rate of the public communication. Our results clarify an essential difference between the key agreement from discrete sources and that from continuous sources.

We consider the distributed source coding system of two correlated Gaussian Vector sources Yl=t(Yl1, Yl2),l=1,2 which are noisy observations of correlated Gaussian scalar source X0. We assume that for each (l,k)∈{1,2}, Ylk is an observation of the source X0, having the form Ylk=X0+Nlk, where Nlk is a Gaussian random variable independent of X0. We further assume that Nlk, (l,k)∈{1,2}2 are independent. In this system two correlated Gaussian observations are separately compressed by two 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 X0. The determination problem of the rate distortion region for this communication system can be regarded as an extension of the Gaussian CEO problem to the case of vector observations. For each vector observation we can obtain an estimation on X0 from this observation. Those estimations are sufficient statistics on X0. Using those sufficient statistics, we determine the rate distortion region by showing that it coincides with the rate distortion region of the CEO problem where the scalar observations of X0 are equal to the estimations computed from the vector observations. We further extend the result to the case of L terminal and general vector observations.

In this paper we analyze the interval algorithm for random number generation proposed by Han and Hoshi in the case of Markov coin tossing. 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 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.

Information leakage in Wyner's wiretap channel model is usually defined as the mutual information between the secret message and the eavesdropper's received signal. We define a new quantity called “conditional information leakage given the eavesdropper's received signals,” which expresses the amount of information that an eavesdropper gains from his/her received signal. A benefit of introducing this quantity is that we can develop a fast algorithm for computing the conditional information leakage, which has linear complexity in the code length n, while the complexity for computing the usual information leakage is exponential in n. Validity of such a conditional information leakage as a security criterion is confirmed by studying the cases of binary symmetric channels and binary erasure channels.

In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R > C. Subsequently, in 1979, Dueck and Körner determined the optimal exponent of correct decoding. Recently the author determined the optimal exponent on the correct probability of decoding have the form similar to that of Dueck and Körner determined. In this paper we give a rigorous proof of the equivalence of the above exponet function of Dueck and Körner to a exponent function which can be regarded as an extention of Arimoto's bound to the case with the cost constraint on the channel input.

Let X, Y be two correlated discrete random variables. We consider an estimation of X from encoded data φ(Y) of Y by some encoder function φ(Y). We derive an inequality describing a relation of the correct probability of estimation and the mutual information between X and φ(Y). This inequality may be useful for the secure analysis of crypto system when we use the success probability of estimating secret data as a security criterion. It also provides an intuitive meaning of the secrecy exponent in the strong secrecy criterion.

In this paper, Information-Spectrum characterization is derived for the reliable transmission of general correlated sources over the general multiple-access channels. We consider the necessary and sufficient conditions for the transmission of general correlated sources over the general multiple-access channels by using Information-Spectrum methods which are introduced by Han and Verdu.

In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R>C. Subsequently, in 1979, Dueck and Körner determined the optimal exponent of correct decoding. Arimoto's bound has been said to be equal to the bound of Dueck and Körner. However its rigorous proof has not been presented so far. In this paper we give a rigorous proof of the equivalence of Arimoto's bound to that of Dueck and Körner.

We consider the problem of constructing nonlinear dynamical systems that realize an arbitrary prescribed tree sources. We give a construction of dynamical systems by using piecewise-linear maps. Furthermore, we examine the obtained dynamical system to show that the structure of the memory of tree sources is characterized with some geometrical property of the constructed dynamical systems. Using a similar method, we also construct a dynamical system generating an arbitrary prescribed reverse tree source and show that the obtained dynamical system has some interesting geometrical property explicitly reflecting the tree structure of the memory of the reverse tree source.

This paper clarifies a necessary condition and a sufficient condition for transmissibility for a given set of general sources and a given general broadcast channel. The approach is based on the information-spectrum methods introduced by Han and Verdu. Moreover, we consider the capacity region of the general broadcast channel with arbitrarily fixed error probabilities if we send independent private and common messages over the channel. Furthermore, we treat the capacity region for mixed broadcast channel.

In this paper we study the large deviation property for chaotic binary sequences generated by one-dimensional maps displaying chaos and thresholds functions. We deal with the case when nonlinear maps are the r-adic maps. The large deviation theory for dynamical systems is useful for investigating this problem.

There are several attempts to generate chaotic binary sequences by using one-dimensional maps. From the standpoint of engineering applications, it is necessary to evaluate statistical properties of sample sequences of finite length. In this paper we attempt to evaluate the statistics of chaotic binary sequences of finite length. The large deviation theory for dynamical systems is useful for investigating this problem.

In 1997, the author considered the separate coding system for two correlated memoryless Gaussian sources and squared distortion measures and determined the rate distortion region in a case where one source plays a role of the partial side information at the decoder. The above source coding system can be extended to a certain class of source network with several decoders, where each decoder has at most one full or partial side information. This class of source network is called the one-helps-one system. In this paper we consider a source network belonging to this class for correlated memoryless Gaussian sources and squared distortion measures. This source network was posed and investigated by Korner and Marton and was called the zig-zag source network. They studied the zig-zag source network in the case of discrete memoryless multiple sources. In this paper we study the zig-zag source network in the case of correlated memoryless Gaussian sources and square distortion. We determine the rate distortion region in a case where sources have a certain correlation property.