Almost all problems in multi-terminal information theory stem from Slepian-Wolf coding problem and a coding problem for multiple access channels (MACs). Cover et al. considered a joint source-channel coding problem and integrated these two problems. One typical example of the communication model proposed by Cover et al. is a sensor network. However, in usual sensor networks, the transmission power of sensors is so small that each sensor cannot send the message to the data center directly, but the nearest relay or edge node, and the relay node resends the message to the data center through a backborn network. We model such a sensor network as MACs employing relay nodes that consist of a cascade of point-to-point channels and a MAC. We show a sufficient condition and a necessary condition for reliable communication over a MAC employing relay nodes. Moreover, we show that both conditions coincide if the sources are independent.

Simulation of random process is one of classic problems in information theory. The simulation problem finds its wide applications in generative AI's, as well as generation of noise for the purpose of simulating various physical systems. We revisit a simulation problem for individual sequences, and propose universal simulation schemes for a given training sequence$x^{n}$with its length$n$. Our goal is to find a good deterministic mapping which generates sequences$y^{n}$simulating$x^{n}$from uniform random numbers. As criteria of good simulation schemes, we deal with the following two conditions: 1)$y^{n}$is statistically similar to$x^{n}$, 2) If$y^{n}$satisfies condition 1), there is as much uncertainty as possible in the choice of$y^{n}$. We propose two simulation schemes based on the interval algorithm which can be executed with the computational complexity of the order$O(n)$. Both schemes satisfy the condition 1), and their output entropy rates are clarified. Further, any simulation scheme which satisfies the condition 1) cannot provide significantly larger output entropy rate than our proposed schemes. This reveals the asymptotical optimality of the proposed simulation schemes.

The Slepian-Wolf (SW) coding system is a source coding system with two encoders and a decoder, where these encoders independently encode source sequences from two correlated sources into codewords, and the decoder reconstructs both source sequences from the codewords. In this paper, we consider the situation in which the SW coding system is asynchronous, i.e., each encoder samples a source sequence with some unknown delay. We assume that delays are unknown but maximum and minimum values of possible delays are known to encoders and the decoder. We also assume that sources are discrete stationary memoryless and the probability mass function (PMF) of the sources is unknown but the system knows that it belongs to a certain set of PMFs. For this asynchronous SW coding system, we clarify the achievable rate region which is the set of rate pairs of encoders such that the decoding error probability vanishes as the blocklength tends to infinity. We show that this region does not always coincide with that of the synchronous SW coding system in which each encoder samples a source sequence without any delay.

This paper addresses the rumor source identification problem, where the goal is to find the origin node of a rumor in a network among a given set of nodes with the rumor. In this paper, we focus on a network represented by a regular tree which does not have any cycle and in which all nodes have the same number of edges connected to a node. For this network, we clarify that, with quite high probability, the origin node is within the distance “3” from the node selected by the optimal estimator, where the distance is the number of edges of the unique path connecting two nodes. This is clarified by the probability distribution of the distance between the origin and the selected node.

In this paper, we consider a source coding with side information partially used at the decoder through a codeword. We assume that there exists a relative delay (or gap) of the correlation between the source sequence and side information. We also assume that the delay is unknown but the maximum of possible delays is known to two encoders and the decoder, where we allow the maximum of delays to be subject to change by the block length. In this source coding, we give an inner bound and an outer bound on the achievable rate region, where the achievable rate region is the set of rate pairs of encoders such that the decoding error probability vanishes as the block length tends to infinity. Furthermore, we clarify that the inner bound coincides with the outer bound when the maximum of delays for the block length converges to a constant.

This paper considers a joint channel coding and random number generation from channel outputs. Specifically, we want to transmit a message to a receiver reliably and at the same time the receiver extracts pure random bits independent of the channel input. We call this problem as the joint channel coding and intrinsic randomness problem. For stationary memoryless channels, we show exponential upper bounds on both the decoding error probability and the variational distance between the distribution of the obtained random number and the uniform distribution. We also clarify that the obtained both bounds vanish as the block length tends to infinity, whenever a pair of coding rate and random bit rate is within the achievable rate region. Further, the above performance can be obtained by a universal scheme which does not depend on the channel.

We normally hold a lot of confidential information in hard disk drives and solid-state drives. When we want to erase such information to prevent the leakage, we have to overwrite the sequence of information with a sequence of symbols that is independent of the information. The overwriting is needed only at places where overwritten symbols are different from original symbols. Then, the cost of overwrites such as the number of overwritten symbols to erase information is important. In this paper, we deal with the worst-case cost which is the cost to erase the most laborious sequence and the average cost which is the expectation of the cost with respect to sequences. We clarify the minimum worst-case cost such that the mutual information between the original sequence and the overwritten sequence normalized by the blocklength of the sequences goes to zero as the blocklength tends to infinity. We also clarify the minimum average cost for stationary memoryless sources in the finite blocklength regime.

This paper deals with a multicast network with a server and many users. The server has content files with the same size, and each user requests one of the files. On the other hand, each user has a local memory, and a part of information of the files is cached (i.e., stored) in these memories in advance of users' requests. By using these cached information as side information, the server encodes files based on users' requests. Then, it sends a codeword through an error-free shared link for which all users can receive a common codeword from the server without error. We assume that the server transmits either of whole or partial information of requested files at each different transmission rate (i.e., the codeword length per file size). In this paper, we focus on the region of pairs of these two rates such that (whole or partial) information of requested files are recovered at each user with an arbitrary small error probability. We give inner and outer bounds on this region.

In this paper, we deal with the fixed-length lossy compression with the ε-fidelity criterion which is a kind of the distortion criterion such that the probability of exceeding a given distortion level is less than a given probability level. We give an achievability bound and a converse bound of the minimum number of codewords with this criterion. We show that our converse bound is tighter than that of Kostina and Verdú. We also show a numerical example which demonstrates that there exists some cases where our achievability bound is tighter than that of Kostina and Verdú.

The key rate of the B92 quantum key distribution protocol had not been reported before this research when the number of qubits is finite. We compute it by using the security analysis framework proposed by Scarani and Renner in 2008.

A source coding system with side information at the decoder is a typical multiterminal source coding system where output sequences of two sources are independently encoded, but a decoder recovers only one output sequence from two codewords. Since Wyner, Ahlswede and Körner independently investigated this system, we call it as the WAK coding system. This paper investigates the ε-achievable rate region of the WAK coding system which allows the probability of error within a fixed tolerance ε(∈ (0, 1)), and clarifies the ε-achievable rate region for correlated general sources in terms of the smooth max-entropy and the smooth max Rényi divergence. To this end, we show a new one-shot converse theorem for the WAK coding system, and a one-shot covering lemma which is a refined version of Warsi's result. Then, combining these results, we clarify the ε-achievable rate region of the WAK coding system.

By extending the notion of minimum rank distance, this paper introduces two new relative code parameters of a linear code C1of length n over a field extension Fqmand its subcode C2⊆ C1. One is called the relative dimension/intersection profile (RDIP), and the other is called the relative generalized rank weight (RGRW). We clarify their basic properties and the relation between the RGRW and the minimum rank distance. As applications of the RDIP and the RGRW, the security performance and the error correction capability of secure network coding, guaranteed independently of the underlying network code, are analyzed and clarified. We propose a construction of secure network coding scheme, and analyze its security performance and error correction capability as an example of applications of the RDIP and the RGRW. Silva and Kschischang showed the existence of a secure network coding in which no part of the secret message is revealed to the adversary even if any dim C1-1 links are wiretapped, which is guaranteed over any underlying network code. However, the explicit construction of such a scheme remained an open problem. Our new construction is just one instance of secure network coding that solves this open problem.

In this paper, we consider a lossy source coding problem with an encoder and two decoders, in which side information is available at one of the decoders with an unknown delay. We assume that the maximum of delay is known to among the encoder and two decoders. In this coding problem, we show upper and lower bounds on the rate-distortion (RD) function, where the RD function is the infimum of rates of codes of which the distortion between the source sequence and the reproduction sequence satisfies a certain distortion level. We also show that the upper bound coincides with the lower bound when the maximum of delay per block length converges to a constant. Furthermore, we show a condition such that the RD function is strictly larger than that for the case of no delay.

This paper clarifies the ε-achievable rate region of the Slepian-Wolf (SW) coding problem for general sources. We propose new upper and lower bounds on the error probability of the SW coding system for finite block lengths. The proposed bounds are mathematically simple and characterized by an optimization problem on the subset of pairs of output sequences which is closely related to the smooth max-entropy, and are tighter than those obtained by Han. By using these bounds, we clarify the ε-achievable rate region. Further, we also show outer and inner bounds on the ε-achievable rate region in terms of the smooth max-entropy. These two bounds coincide when the error probability vanishes.

This paper clarifies the rate-distortion function for general sources in terms of the smooth max Rényi divergence. To this end, we investigate the fixed-length coding problem with two kinds of distortion criteria. One criterion is the maximum distortion criterion, and the other is the average distortion criterion. We show a new achievability result for the latter criterion and new meta-converse theorems for both criteria, and clarify the rate-distortion functions in terms of the smooth Rényi divergence instead of the spectral mutual information.

Weissman introduced a channel coding problem for channels with action-dependent states. In this coding problem, there are two encoders and a decoder. One encoder outputs an action that affects states of the channel. Then, the other encoder encodes a message by using the channel state, and its codeword is fed into the channel. The decoder receives a noisy observation of the codeword, and reconstructs the message. For this coding problem, Weissman showed the capacity when states and the channel are stationary memoryless. In this paper, we show a general formula of the capacity when states and the channel may not be stationary memoryless, which is expressed by mutual information spectrum-sup/inf proposed by Verdú and Han. Our general formula coincides with the capacity derived by Tan when actions cannot affect states of channels. We also show that the capacity for nonstationary memoryless channels can be expressed by using ordinary mutual information.

The purpose of this paper is to establish a new unified method for random number generation from general sources. Specifically, we introduce an alternative definition of the smooth Rényi entropy of order infinity, and show a unified approach to represent the intrinsic randomness in terms of this information quantity. Our definition of the smooth Rényi entropy is easy to calculate for finite block lengths. We also represent δ-intrinsic randomness and the strong converse property in terms of the smooth Rényi entropy.

The universal strongly secure network coding scheme allows communication at maximum rate while ensuring that, independently from the underlying network code, no part of the secret message is revealed to the wiretapper. Although Silva and Kschischang showed the existence of such a scheme, the explicit construction remained an open question. This paper demonstrates an explicit construction of the scheme that uses secret sharing schemes based on maximum rank distance (MRD) codes, which can be viewed as a special case of Ozarow-Wyner coset coding scheme.

Heegard and Berger introduced the model of lossy source coding in which side information is available at many decoders. For this model, their showed an upper bound of the rate-distortion function in the case where the source is stationary memoryless. In this paper, we extend their model to the case where the source may be nonstationary and/or nonergodic, and clarify the rate-distortion function for this model. This result is based on the information-spectrum method introduced by Han and Verdú. We also show some special cases of the rate-distortion function, and a single-letterized upper bound of the rate-distortion function in the case where the source is stationary memoryless.

A multiterminal lossy source coding problem, which includes various problems such as the Wyner-Ziv problem and the complementary delivery problem as special cases, is considered. It is shown that any point in the achievable rate-distortion region can be attained even if the source statistics are not known.

Low-density parity-check (LDPC) codes become very popular in channel coding, since they can achieve the performance close maximum-likelihood (ML) decoding with linear complexity of the block length. Muramatsu et al. proposed a code using LDPC matrices for Slepian-Wolf source coding. However, since they employed ML decoding, their code is not universal, that is their decoder needs to know the probability distribution of the source. On the other hand, if there exists a universal code using LDPC matrices, we can arbitrary decrease the error probability for all sources whose achievable rate region contains the rate pair of encoders even if the probability distribution of sources is unknown. To this end, we show the existence of a universal Slepian-Wolf source code using LDPC matrices in the case where the source is stationary memoryless.

We improve the non-asymptotic key rate shown by Scarani and Renner by proposing several methods to construct tighter conservative confidence interval of the phase error rate than the one shown by them. In addition, we show that the accurate channel estimation method non-asymptotically increases the key rate over the amplitude damping channel as well as the asymptotic case in the BB84 protocol.

Silva et al. proposed a universal secure network coding scheme based on MRD codes, which can be applied to any underlying network code. This paper considers a stronger eavesdropping model where the eavesdroppers possess the ability to re-select the tapping links during the transmission. We give a proof for the impossibility of attaining universal security against such adversaries using Silva et al.'s code for all choices of code parameters, even with restricted number of tapped links. We also consider the cases with restricted tapping duration and derive some conditions for this code to be secure.

This paper deals with the resolvability problem for general sources, and establishes a new unified method for the resolvability problem of general sources. Specifically, we introduce Shannon's information measure for fixed length source coding, and show a unified method to present the resolvability in terms of this information quantity. Further, we also represent δ-resolvability of general sources and the strong converse property in terms of Shannon's information measure.

We consider energy savings offered by network coding for multiple unicast in wireless networks. For d-dimensional wireless networks we show that the maximum possible benefit is at least 2d/¿¿d¿.

Wyner's source coding system is one of the most fundamental fixed-length source coding systems with side information available only at the decoder. In this coding system, Wyner showed the achievable rate region which is the set of rate pairs of encoders such that the probability of error can be made arbitrarily small for sufficiently large block length. However, the closed form of this region is not clarified because the region is expressed by the union of indefinitely many sets. This paper deals with two correlated sources whose conditional distribution is represented by binary input output symmetric channels, and clarifies closed forms of the achievable rate region for Wyner's source coding system.

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.

This paper deals with a universal lossy coding problem for a certain kind of multiterminal source coding network called a complementary delivery system. A universal coding scheme based on Wyner-Ziv codes is proposed. While the proposed scheme cannot attain the optimal rate-distortion trade off in general, the rate-loss is upper bounded by a universal constant under some mild conditions. Moreover, the proposed scheme allows us to apply (non-universal) Wyner-Ziv codes to construct a universal lossy complementary delivery code.

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 Dijkstra’s algorithm with bounded list size after QR decomposition for decreasing the computational complexity of near maximum-likelihood (ML) detection of signals over multiple-input-multiple-output (MIMO) channels. After that, we compare the performances of proposed algorithm, QR decomposition M-algorithm (QRM-MLD), and its improvement. When the list size is set to achieve the almost same symbol error rate (SER) as the QRM-MLD, the proposed algorithm has smaller average computational complexity.

Relay channels are known as a model of multihop wireless networks which are often studied. In relay channels, the sender sends a message to the relay and the receiver, the relay encodes the channel output again and forwards it to the receiver, and the receiver decodes the message from the channel output. This paper deals with the universal coding problem for relay channels. First, we propose two new decoders based on the maximum mutual information decoder and show the existence of a universal code for relay channels by combining the proposed decoders and the coding scheme obtained by Cover and El Gamal. Second, we clarify the condition that the probability of error for each decoder decreases exponentially as the block length tends to infinity. Finally, we prove that the proposed universal code achieves the capacity of the degraded relay channel.

Consider a source network in which a finite alphabet source X = {Xi}i=0infinis to be encoded and transmitted, and another finite alphabet source Y = {Xi}i=0infincorrelated with X is available only to the decoder as side information. Traditionally, the channel between the encoder and decoder in the source network is assumed to be one-way. This, together with the fact that the encoder does not have access to Y, implies that the encoder has to know the achievable rates before encoding. In this paper, we consider universal source coding for a feedback source network in which the channel between the encoder and decoder is two-way and asymmetric. Assume that the encoder and decoder share a random database that is independent of both X and Y. A string matching-based (variable-rate) block coding algorithm with simple progressive encoding and joint typicality decoding is first proposed for the feedback source network. The simple progressive encoder does not need to know the achievable rates at the beginning of encoding. It is proven that for any (X, Y) in a large class of sources satisfying some mixing conditions, the average number of bits per letter transmitted from the encoder to the decoder (compression rate) goes to the conditional entropy H(X | Y) of X given Y asymptotically, and at the same time the average number of bits per letter transmitted from the decoder to the encoder (feedback rate) goes to 0 asymptotically. The algorithm and the corresponding analysis results are then extended to the case where both X and Y are to be encoded separately, but decoded jointly. Finally, a universal decoding algorithm is proposed to replace the joint typicality decoding, and the resulting universal compression algorithm consisting of the simple progressive encoder and the universal decoding algorithm is further shown to be asymptotically optimal for the class of all jointly memoryless source-side information pairs (X,Y).

This report deals with a universal coding problem for a certain kind of multiterminal source coding system that we call the complementary delivery coding system. 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 via type-theoretical and graph-theoretical analyses.

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).

Let$N(d,d^perp)$denote the minimum length$n$of a linear code$C$with$d$and$d^bot$, where$d$is the minimum Hamming distance of$C$and$d^bot$is the minimum Hamming distance of$C^bot$. In this correspondence, we show lower bounds and an upper bound on$N(d,d^perp)$. Further, for small values of$d$and$d^perp$, we determine$N(d,d^perp)$and give a generator matrix of the optimum linear code. This problem is directly related to the design method of cryptographic Boolean functions suggested by Kurosawa

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.

Consider a source network in which a finite alphabet source X = {Xi}iinfin=0is to be encoded and transmitted, and another finite alphabet source Y = {Yi}iinfin=0available only to the decoder as the side information correlated with X. Traditionally the channel between the encoder and decoder in the source network is assumed to be one-way. This, together with that the encoder does not have access to Y, necessitates that the encoder knows the achievable rates before encoding. In this paper we consider universal source coding for a feedback source network in which the channel between the encoder and decoder is two-way and asymmetric. Assuming that the encoder and decoder share a random database that is independent of both X and Y, we propose a string matching-based (variable-rate) block coding algorithm with a simple progressive encoder for the feedback source network. This algorithm does not need to know the achievable rates at the beginning of encoding. It is proven that for any (X, Y) in a large class of sources which includes the class of all memoryless sources, the class of all aperiodic Markov sources, and a large class of finite-state sources as special subclasses, the average number of bits per letter transmitted from the encoder to the decoder (compression rate) goes arbitrarily close to the conditional entropy H(X|Y) of X given Y asymptotically, and the average number of bits per letter transmitted from the decoder to the encoder (feedback rate) goes to 0 asymptotically

Dealing with the explosive increase in the amount of Internet traffic requires high-speed and huge capacity Internet protocol (IP) backbone networks. Existing IP backbone networks are constructed using point-to-point wavelength-division-multiplexing (WDM) transmission systems, where all the wavelengths are terminated link-by-link, so that rather expensive optical/electrical conversions are necessary at every node. In these systems, since every IP packet is routed at each intermediate node based on the header information, a header processing bottleneck will occur when the node input traffic exceeds several hundreds of gigabits per second. In order to mitigate these problems, an optical cross-connect (OXC) function that employs wavelength routing of the optical paths (OPs) will provide an effective solution. This paper proposes a network design method where electrical and photonic multiprotocol label switching (MPLS) technologies are used; the network is referred to as a photonic IP network. We first propose new algorithms that minimize the network cost in a multilayered network comprising electrical label switched paths (LSPs) and optical LSPs (optical paths that are controlled using the MPLS mechanism). The particular point of the proposed algorithms is that they include different cost minimization scenarios appropriate for the different OLSP provisioning conditions that are chosen as the first step in the design stage. The effectiveness of the proposed algorithms and the benefits of the OLSPs are quantitatively evaluated through various simulations.

Linear codes for a coding problem of correlated sources are considered. It is proved that we can construct codes by using low-density parity-check (LDPC) matrices with maximum-likelihood (or typical set) decoding. As applications of the above coding problem, a construction of codes is presented for multiple-access channel with correlated additive noises and a coding theorem of parity-check codes for general channels is proved.

Coding problems for correlated information sources were first investigated by Slepian and Wolf. They considered the data compression system, called the SW system, where two sequences emitted from correlated sources are separately encoded to codewords, and sent to a single decoder which has to output the original sequence pairs with a small probability or error. In this paper, we investigate the coding problem of a modified SW system allowing two encoders to communicate with zero rate. First, we consider the fixed-length coding and clarify that the admissible rate region for general sources is equal to that of the original SW system. Next, we investigate the variable-length coding having the asymptotically vanishing probability of error. We clarify the admissible rate region for mixed sources characterized by two ergodic sources and show that this region is strictly wider than that for fixed-length codes. Further, we investigate the universal coding problem for memoryless sources in the system and show that the SW system with linked encoders has much more flexibility than the original SW system.

The paper considers linear matrices for a coding problem for multiple access networks. It is proved that we can construct codes by using sparse matrices, which are also called low density parity check (LDPC) matrices.

Slepian and Wolf (see IEEE Trans. Inform. Theory, vol.19, p.471-80, July 1973) first considered the data compression of correlated sources called the SW system, where two sequences emitted from correlated sources are separately encoded to codewords, and sent to a single decoder which has to output original sequence pairs. Recently, Oohama (see IEEE Trans. Inform. Theory, vol.42, p.837-47, May 1996) has extended the SW system and investigated a more general case where there are some mutual linkages between two encoders of the SW system. In this paper, we investigate variable-length coding which allows asymptotically vanishing probability of error for the system considered by Oohama. We clarify the admissible rate region for mixed sources characterized by two ergodic sources, and show that this region is strictly wider than that for fixed-length codes.

This article proposes an explicit construction of fixed-length codes for Slepian-Wolf (1973) source networks. The proposed code is linear, and has two-step encoding and decoding procedures similar to the concatenated code used for channel coding. Encoding and decoding of the code can be done in a polynomial order of the block length. The proposed code can achieve arbitrary small probability of error for ergodic sources with finite alphabets, if the pair of encoding rates is in the achievable region. Further, if the sources are memoryless, the proposed code can be modified to become universal and the probability of error vanishes exponentially as the block length tends to infinity.

This article deals with the problem of simulating a discrete memoryless channel and proposes two algorithms for channel simulation by using the interval algorithm. The first algorithm provides exact channel simulation and the number of fair random bits per input sample approaches the conditional resolvability of the channel with probability one. The second algorithm provides approximate channel simulation and the approximation error measured by the variational distance vanishes exponentially as the block length tends to infinity, when the number of fair random bits per input sample is above the conditional resolvability. Further, some asymptotic properties of these algorithms as well as the original interval algorithm for random number generation are clarified.

This correspondence proposes an explicit construction of codes achieving capacity for arbitrary discrete memoryless channels. The proposed code is obtained by concatenating variable inner codes and an algebraic geometry code. Further, we clarify that the proposed code achieves the error exponent obtained by Forney for concatenated codes.

Quantum communication with a nonsymmetrical set of three states is considered. Some results obtained from numerical computation are presented. A model for quantum detection called "near optimum", similar to the binary case, is studied. Calculations of error probability in detection schemes subject to information criteria are performed and discussed. Further, comparison of the error probability in detection between these different schemes is analyzed.>

This paper presents a hierarchical classification of signals based on their smoothness. By this hierarchical classification, we can obtain the class of bandlimited signals as an innermost signal class and the class of signals composed of differentiable and square integrable functions as the outermost class. Moreover, for each class of signals, we can define "minimum norm signal". The minimum norm signal is defined as the signal of minimum norm which takes specified sample values on a set of given sampling points. By making use of the minimum norm signal, we can construct a unified and efficient approximation method for all these classes of signals. The method has the following special features: i) it is free from numerical integration error, ii) the sequence of approximate signals is guaranteed to uniformly converge to the desired signal as the number of sampling points is increased infinitely.