arXiv subjects

Te Sun Han

Publications and source records attributed to Te Sun Han.

At least 19 recordsLinked to original sources

arXiv2025

Path-Controlled Secure Network Coding

Multicast for securely sharing confidential data among many users is becoming increasingly important. Currently, it relies on duplicate-and-forward routing and cryptographic methods based on computational security. However, these approaches neither attain multicast capacity of the network, nor ensure long-term security against advances in computing (information-theoretic security: ITS). Existing ITS solutions--quantum key distribution (QKD), physical layer security (PLS), and secure network coding (SNC)--still fail to enable scalable networks, as their underlying assumptions, such as trusted nodes and wiretap thresholds, gradually become invalid as the network grows. Here, we develop an efficient multi-tree multicast path-finding method to address this issue, integrating it with universal strongly ramp SNC. This system, path-controlled universal strongly ramp SNC (PUSNEC), can be overlaid onto QKD/PLS networks, enabling multicast capacity, ITS, and scalability. We derive the maximum leakage information to an eavesdropper under the probabilistic wiretap network assumption and demonstrate secure multicast in multi-hop networks through numerical simulations. Our quantitative analysis of the secrecyreliability tradeoff highlights a practical approach to achieving secure, reliable multicast on a global scale.

cs.IT↗

arXiv2020

Isomorphism Problem Revisited: Information Spectrum Approach

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 \v{S}ujan, 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.

cs.IT↗

arXiv2020

Wiretap channels with causal and non-causal state information: revisited

The coding problem for wiretap channels with causal channel state information (CSI) available at the encoder (Alice) and/or the decoder (Bob) is studied. We are concerned here particularily with the problem of achievable secret-message secret-key rate pairs under the semantic security criterion. Our main result extends all the previous results on achievable rates as given by Chia and El Gamal [10], Fujita [11], and Han and Sasaki [23]. In order to do this, we first derive a unifying theorem (Theorem 2) with causal CSI at Alice, which follows immediately by leveraging the unifying seminal theorem for wiretap channels with non-causal CSI at Alice as recently established by Bunin et al. [22]. The only thing to do here is just to re-interpret the latter non-causal one in a causal manner. A prominent feature of this approach is that we are able to dispense with the block-Markov encoding scheme as used in the previous works. Also, the exact secret-message key capacity region for wiretap channels with non-causal CSI at both Alice and Bob is given.

cs.IT↗

arXiv2019

Interval Algorithm for Random Number Generation: Information Spectrum Approach

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 the perspective of information spectrum approach. When either the coin process or the target process has one point spectrum, the 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. Furthermore, the feasibility condition of exact random number generation is also elucidated. Finally, the obtained general results are illustrated by the case of generating a Markov process from another Markov process.

cs.IT↗

arXiv2018

Variable-Length Resolvability for Mixed Sources and its Application to Variable-Length Source Coding

In the problem of variable-length $\delta$-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated distributions should be within a given constant $\delta$ asymptotically. In this paper, we assume that the given channel input is a mixed source whose components may be general sources. To analyze the minimum achievable length rate of the uniform random number, called the $\delta$-resolvability, we introduce a variant problem of the variable-length $\delta$-channel resolvability. A general formula for the $\delta$-resolvability in this variant problem is established for a general channel. When the channel is an identity mapping, it is shown that the $\delta$-resolvability in the original and variant problems coincide. This relation leads to a direct derivation of a single-letter formula for the $\delta$-resolvability when the given source is a mixed memoryless source. We extend the result to the second-order case. As a byproduct, we obtain the first-order and second-order formulas for fixed-to-variable length source coding allowing error probability up to $\delta$.

cs.IT↗

arXiv2017

Wiretap Channels with Causal State Information: Strong Secrecy

The coding problem for wiretap channels with causal channel state information available at the encoder and/or the decoder is studied under the strong secrecy criterion. This problem consists of two aspects: one is due to naive wiretap channel coding and the other is due to one-time pad cipher based on the secret key agreement between Alice and Bob using the channel state information. These two aspects are closely related to each other and investigated in details from the viewpoint of achievable rates with strong secrecy. The general wiretap channel with various directions of channel state informations among Alice, Bob and Eve (called the multi-way channel state information) is also studied, which includes the above systems as special cases. We provide a unified view about wiretap channel coding with causal multi-way channel state information.

cs.IT↗

arXiv2017

First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources with General Mixture

The first- and second-order optimum achievable exponents in the simple hypothesis testing problem are investigated. The optimum achievable exponent for type II error probability, under the constraint that the type I error probability is allowed asymptotically up to epsilon, is called the epsilon-optimum exponent. In this paper, we first give the second-order epsilon-exponent in the case where the null hypothesis and the alternative hypothesis are a mixed memoryless source and a stationary memoryless source, respectively. We next generalize this setting to the case where the alternative hypothesis is also a mixed memoryless source. We address the first-order epsilon-optimum exponent in this setting. In addition, an extension of our results to more general setting such as the hypothesis testing with mixed general source and the relationship with the general compound hypothesis testing problem are also discussed.

cs.IT↗

arXiv2017

Variable-Length Resolvability for General Sources and Channels

We introduce the problem of variable-length source resolvability, where a given target probability distribution is approximated by encoding a variable-length uniform random number, and the asymptotically minimum average length rate of the uniform random numbers, called the (variable-length) resolvability, is investigated. We first analyze the variable-length resolvability with the variational distance as an approximation measure. Next, we investigate the case under the divergence as an approximation measure. When the asymptotically exact approximation is required, it is shown that the resolvability under the two kinds of approximation measures coincides. We then extend the analysis to the case of channel resolvability, where the target distribution is the output distribution via a general channel due to the fixed general source as an input. The obtained characterization of the channel resolvability is fully general in the sense that when the channel is just the identity mapping, the characterization reduces to the general formula for the source resolvability. We also analyze the second-order variable-length resolvability.

cs.IT↗

arXiv2016

First- and Second-Order Coding Theorems for Mixed Memoryless Channels with General Mixture

This paper investigates the first- and second-order maximum achievable rates of codes with/without cost constraints for mixed {channels} whose channel law is characterized by a general mixture of (at most) uncountably many stationary and memoryless discrete channels. These channels are referred to as {mixed memoryless channels with general mixture} and include the class of mixed memoryless channels of finitely or countably memoryless channels as a special case. For mixed memoryless channels with general mixture, the first-order coding theorem which gives a formula for the $\varepsilon$-capacity is established, and then a direct part of the second-order coding theorem is provided. A subclass of mixed memoryless channels whose component channels can be ordered according to their capacity is introduced, and the first- and second-order coding theorems are established. It is shown that the established formulas reduce to several known formulas for restricted scenarios.

cs.IT↗

arXiv2015

Numerical Study on Secrecy Capacity and Code Length Dependence of the Performances in Optical Wiretap Channels

Secrecy issues of free-space optical links realizing information theoretically secure communications as well as high transmission rates are discussed. We numerically study secrecy communication rates of optical wiretap channel based on on-off keying modulation under typical conditions met in satellite-ground links. It is shown that under reasonable degraded conditions on a wiretapper, information theoretically secure communications should be possible in a much wider distance range than a range limit of quantum key distribution, enabling secure optical links between geostationary earth orbit satellites and ground stations with currently available technologies. We also provide the upper bounds on the decoding error probability and the leaked information to estimate a necessary code length for given required levels of performances. This result ensures that a reasonable length wiretap channel code for our proposed scheme must exist.

cs.IT↗

arXiv2014

Reliability and Secrecy Functions of the Wiretap Channel under Cost Constraint

The wiretap channel has been devised and studied first by Wyner, and subsequently extended to the case with non-degraded general wiretap channels by Csiszar and Korner. Focusing mainly on the Poisson wiretap channel with cost constraint, we newly introduce the notion of reliability and security functions as a fundamental tool to analyze and/or design the performance of an efficient wiretap channel system. Compact formulae for those functions are explicitly given for stationary memoryless wiretap channels. It is also demonstrated that, based on such a pair of reliability and security functions, we can control the tradeoff between reliability and security (usually conflicting), both with exponentially decreasing rates as block length n becomes large. Two ways to do so are given on the basis of concatenation and rate exchange. In this framework, the notion of the δ secrecy capacity is defined and shown to attain the strongest security standard among others. The maximized vs. averaged security measures is also discussed.

cs.IT↗

arXiv2012

Second-Order Slepian-Wolf Coding Theorems for Non-Mixed and Mixed Sources

The second-order achievable rate region in Slepian-Wolf source coding systems is investigated. The concept of second-order achievable rates, which enables us to make a finer evaluation of achievable rates, has already been introduced and analyzed for general sources in the single-user source coding problem. Analogously, in this paper, we first define the second-order achievable rate region for the Slepian-Wolf coding system to establish the source coding theorem in the second- order sense. The Slepian-Wolf coding problem for correlated sources is one of typical problems in the multi-terminal information theory. In particular, Miyake and Kanaya, and Han have established the first-order source coding theorems for general correlated sources. On the other hand, in general, the second-order achievable rate problem for the Slepian-Wolf coding system with general sources remains still open up to present. In this paper we present the analysis concerning the second- order achievable rates for general sources which are based on the information spectrum methods developed by Han and Verdu. Moreover, we establish the explicit second-order achievable rate region for i.i.d. correlated sources with countably infinite alphabets and mixed correlated sources, respectively, using the relevant asymptotic normality.

cs.IT↗

arXiv2012

Second-Order Resolvability, Intrinsic Randomness, and Fixed-Length Source Coding for Mixed Sources: Information Spectrum Approach

The second-order achievable asymptotics in typical random number generation problems such as resolvability, intrinsic randomness, fixed-length source coding are considered. In these problems, several researchers have derived the first-order and the second-order achievability rates for general sources using the information spectrum methods. Although these formulas are general, their computation are quite hard. Hence, an attempt to address explicit computation problems of achievable rates is meaningful. In particular, for i.i.d. sources, the second-order achievable rates have earlier been determined simply by using the asymptotic normality. In this paper, we consider mixed sources of two i.i.d. sources. The mixed source is a typical case of nonergodic sources and whose self-information does not have the asymptotic normality. Nonetheless, we can explicitly compute the second-order achievable rates for these sources on the basis of two-peak asymptotic normality. In addition, extensions of our results to more general mixed sources, such as a mixture of countably infinite i.i.d. sources or Markovian sources, and a continuous mixture of i.i.d. sources, are considered.

cs.IT↗

arXiv2010

Polymatroids with Network Coding

The problem of network coding for multicasting a single source to multiple sinks has first been studied by Ahlswede, Cai, Li and Yeung in 2000, in which they have established the celebrated max-flow mini-cut theorem on non-physical information flow over a network of independent channels. On the other hand, in 1980, Han has studied the case with correlated multiple sources and a single sink from the viewpoint of polymatroidal functions in which a necessary and sufficient condition has been demonstrated for reliable transmission over the network. This paper presents an attempt to unify both cases, which leads to establish a necessary and sufficient condition for reliable transmission over a noisy network for multicasting all the correlated multiple sources to all the multiple sinks. Furthermore, we address also the problem of transmitting "independent" sources over a multiple-access-type of network as well as over a broadcast-type of network, which reveals that the (co-) polymatroidal structures are intrinsically involved in these types of network coding.

cs.IT↗

arXiv2010

Multicasting correlated multi-source to multi-sink over a network

The problem of network coding with multicast of a single source to multisink has first been studied by Ahlswede, Cai, Li and Yeung in 2000, in which they have established the celebrated max-flow mini-cut theorem on non-physical information flow over a network of independent channels. On the other hand, in 1980, Han has studied the case with correlated multisource and a single sink from the viewpoint of polymatroidal functions in which a necessary and sufficient condition has been demonstrated for reliable transmission over the network. This paper presents an attempt to unify both cases, which leads to establish a necessary and sufficient condition for reliable transmission over a network multicasting correlated multisource to multisink. Here, the problem of separation of source coding and channel coding is also discussed.

cs.IT↗

arXiv2007

Joint Source-Channel Coding Revisited: Information-Spectrum Approach

Given a general source with countably infinite source alphabet and a general channel with arbitrary abstract channel input/channel output alphabets, we study the joint source-channel coding problem from the information-spectrum point of view. First, we generalize Feinstein's lemma (direct part) and Verdu-Han's lemma (converse part) so as to be applicable to the general joint source-channel coding problem. Based on these lemmas, we establish a sufficient condition as well as a necessary condition for the source to be reliably transmissible over the channel with asymptotically vanishing probability of error. It is shown that our sufficient condition is equivalent to the sufficient condition derived by Vembu, Verdu and Steinberg, whereas our necessary condition is shown to be stronger than or equivalent to the necessary condition derived by them. It turns out, as a direct consequence, that separation principle in a relevantly generalized sense holds for a wide class of sources and channels, as was shown in a quite dfifferent manner by Vembu, Verdu and Steinberg. It should also be remarked that a nice duality is found between our necessary and sufficient conditions, whereas we cannot fully enjoy such a duality between the necessary condition and the sufficient condition by Vembu, Verdu and Steinberg. In addition, we demonstrate a sufficient condition as well as a necessary condition for the epsilon-transmissibility. Finally, the separation theorem of the traditional standard form is shown to hold for the class of sources and channels that satisfy the semi-strong converse property.

cs.IT↗

arXiv2006

An information-spectrum approach to large deviation theorems

In this paper we show a some new look at large deviation theorems from the viewpoint of the information-spectrum (IS) methods, which has been first exploited in information theory, and also demonstrate a new basic formula for the large deviation rate function in general, which is a pair of the lower and upper IS rate functions. In particular, we are interested in establishing the general large deviation rate functions that can be derivable as the Fenchel-Legendre transform of the cumulant generating function. The final goal is to show a necessary and sufficient condition for the rate function to be of Cramér-Gärtner-Ellis type.

cs.IT↗

arXiv2000

An information-spectrum approach to joint source-channel coding

Given a general source $\sV=\{V^n\}\noi$ with {\em countably infinite} source alphabet and a general channel $\sW=\{W^n\}\noi$ with arbitrary {\em abstract} channel input and output alphabets, we study the joint source-channel coding problem from the information-spectrum point of view. First, we generalize Feinstein's lemma (direct part) and Verdú-Han's lemma (converse part) so as to be applicable to the general joint source-channel coding problem. Based on these lemmas, we establish a sufficient condition as well as a necessary condition for the source $\sV$ to be reliably transmissible over the channel $\sW$ with asymptotically vanishing probability of error. It is shown that our sufficient condition coincides with the sufficient condition derived by Vembu, Verdú and Steinberg, whereas our necessary condition is much stronger than the necessary condition derived by them. Actually, our necessary condition coincide with our sufficient condition if we disregard some asymptotically vanishing terms appearing in those conditions. Also, it is shown that {\em Separation Theorem} in the generalized sense always holds. In addition, we demonstrate a sufficient condition as well as a necessary condition for the $\vep$-transmissibility ($0\le \vep <1$). Finally, the separation theorem of the traditional standard form is shown to hold for the class of sources and channels that satisfy the (semi-) strong converse property.

math.PR↗