Yasutada Oohama

The rate-distortion function for the quadratic Gaussian CEO problem

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.

Gaussian multiterminal source coding

We consider the problem of separate coding for two correlated memoryless Gaussian source. We determine the rate-distortion region in a special case that one source plays a role of partial side information to reproduce sequences emitted from the other source with a prescribed average distortion level. We also derive an explicit outer bound of the rate-distortion region, demonstrating that the inner bound obtained by Berger (1978) partially coincides with the rate-distortion region.

Rate-distortion theory for Gaussian multiterminal source coding systems with several side informations at the decoder

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

Coding for relay channels with confidential messages

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.

Capacity Theorems for Relay Channels with Confidential Messages

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.

Universal coding for the Slepian-Wolf data compression system and the strong converse theorem

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. >

Secret Key Agreement From Vector Gaussian Sources by Rate Limited Public Communication

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.

Distributed Source Coding of Correlated Gaussian Remote Sources

We consider the distributed source coding system for L correlated memoryless Gaussian remote sources specified with L correlated Gaussian random variables Xi, i=1,2,...,L. We deal with the case where each of L distributed encoders cannot directly observe the source Xi but its noisy version Yi=Xi+Ni. Here, Ni, i=1,2,..., L are independent additive L 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 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.

Gaussian Multiterminal Source Coding with Several Side Informations at the Decoder

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 authors 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

Universal coding for correlated sources with linked encoders

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.