arXiv subjects

Hirosuke Yamamoto

Publications and source records attributed to Hirosuke Yamamoto.

At least 19 recordsLinked to original sources

arXiv2026

Asymmetric Encoding-Decoding Schemes for Lossless Data Compression

This paper proposes a new lossless data compression coding scheme named an asymmetric encoding-decoding scheme (AEDS), which can be considered as a generalization of tANS (tabled variant of asymmetric numeral systems). In the AEDS, a data sequence $\mathbf{s}=s_1s_2\cdots s_n$ is encoded in backward order $s_t, t=n, \cdots, 2,1$, while $\mathbf{s}$ is decoded in forward order $s_t, t=1, 2, \cdots, n$ in the same way as the tANS. But, the code class of the AEDS is much broader than that of the tANS. We show for i.i.d.~sources that an AEDS with 2 states (resp.~5 states) can attain a shorter average code length than the Huffman code if a child of the root in the Huffman code tree has a probability weight larger than 0.61803 (resp.~0.56984). Furthermore, we derive several upper bounds on the average code length of the AEDS, which also hold for the tANS, and we show that the average code length of the optimal AEDS and tANS with $N$ states converges to the source entropy with speed $O(1/N)$ as $N$ increases.

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arXiv2024

Encoding and Decoding Algorithms of ANS Variants and Evaluation of Their Average Code Lengths

Asymmetric Numeral Systems (ANS) proposed by Jarek Duda are high-performance distortionless data compression schemes that can achieve almost the same compression performance as arithmetic codes with less arithmetic operations than arithmetic coding. The ANS is widely used in various practical systems like Facebook, Apple, Google, Dropbox, Microsoft, and Pixar, due to their high performance, but many researchers still lack much knowledge about the ANS. This paper thoroughly explains the encoding and decoding algorithms of the ANS, and theoretically analyzes the average code length achievable by the ANS.

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arXiv2019

On the Capacity of Symmetric $M$-user Gaussian Interference Channels with Feedback

A general time-varying feedback coding scheme is proposed for $M$-user fully connected symmetric Gaussian interference channels. Based on the analysis of the general coding scheme, we prove a theorem which gives a criterion for designing good time-varying feedback codes for Gaussian interference channels. The proposed scheme improves the Suh-Tse and Kramer inner bounds of the channel capacity for the cases of weak and not very strong interference when $M=2$. This capacity improvement is more significant when the signal-to-noise ratio (SNR) is not very high. In addition, our coding scheme can be proved mathematically and numerically to outperform the Kramer code for $M\geq 2$ when Signal to Noise Ratio (SNR) is equal to Interference to Noise Ratio (INR). Besides, the generalized degrees-of-freedom (GDoF) of our proposed coding scheme can be proved to be optimal in the all network situations (very weak, weak, strong, very strong) for any $M$. The numerical results show that our coding scheme can attain better performance than the Suh-Tse coding scheme for $M=2$ or the Mohajer-Tandon-Poor lattice coding scheme for $M>2$. Furthermore, the simplicity of the encoding/decoding algorithms is another strong point of our proposed coding scheme compared with the Suh-Tse coding scheme when $M=2$ and the Mohajer-Tandon-Poor lattice coding scheme when $M>2$. More importantly, our results show that an optimal coding scheme for the symmetric Gaussian interference channels with feedback can be achieved by only using marginal posterior distributions under a better cooperation strategy between transmitters.

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arXiv2019

Proceedings of the 11th Asia-Europe Workshop on Concepts in Information Theory

This year, 2019 we celebrate 30 years of our friendship between Asian and European scientists at the AEW11 in Rotterdam, the Netherlands. Many of the 1989 participants are also present at the 2019 event. This year we have many participants from different parts of Asia and Europe. It shows the importance of this event. It is a good tradition to pay a tribute to a special lecturer in our community. This year we selected Hiroyoshi Morita, who is a well known information theorist with many original contributions.

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arXiv2017

Worst-case Redundancy of Optimal Binary AIFV Codes and their Extended Codes

Binary AIFV codes are lossless codes that generalize the class of instantaneous FV codes. The code uses two code trees and assigns source symbols to incomplete internal nodes as well as to leaves. AIFV codes are empirically shown to attain better compression ratio than Huffman codes. Nevertheless, an upper bound on the redundancy of optimal binary AIFV codes is only known to be 1, which is the same as the bound of Huffman codes. In this paper, the upper bound is improved to 1/2, which is shown to coincide with the worst-case redundancy of the codes. Along with this, the worst-case redundancy is derived in terms of $p_{\max}\geq$1/2, where $p_{\max}$ is the probability of the most likely source symbol. Additionally, we propose an extension of binary AIFV codes, which use $m$ code trees and allow at most $m$-bit decoding delay. We show that the worst-case redundancy of the extended binary AIFV codes is $1/m$ for $m \leq 4.$

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arXiv2017

Proceedings of Workshop AEW10: Concepts in Information Theory and Communications

The 10th Asia-Europe workshop in "Concepts in Information Theory and Communications" AEW10 was held in Boppard, Germany on June 21-23, 2017. It is based on a longstanding cooperation between Asian and European scientists. The first workshop was held in Eindhoven, the Netherlands in 1989. The idea of the workshop is threefold: 1) to improve the communication between the scientist in the different parts of the world; 2) to exchange knowledge and ideas; and 3) to pay a tribute to a well respected and special scientist.

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arXiv2017

Variable-to-Fixed Length Homophonic Coding Suitable for Asymmetric Channel Coding

In communication through asymmetric channels the capacity-achieving input distribution is not uniform in general. Homophonic coding is a framework to invertibly convert a (usually uniform) message into a sequence with some target distribution, and is a promising candidate to generate codewords with the nonuniform target distribution for asymmetric channels. In particular, a Variable-to-Fixed length (VF) homophonic code can be used as a suitable component for channel codes to avoid decoding error propagation. However, the existing VF homophonic code requires the knowledge of the maximum relative gap of probabilities between two adjacent sequences beforehand, which is an unrealistic assumption for long block codes. In this paper we propose a new VF homophonic code without such a requirement by allowing one-symbol decoding delay. We evaluate this code theoretically and experimentally to verify its asymptotic optimality.

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arXiv2016

Posterior Matching for Gaussian Broadcast Channels with Feedback

In this paper, the posterior matching scheme proposed by Shayevits and Feder is extended to the Gaussian broadcast channel with feedback, and the error probabilities and achievable rate region are derived for this coding strategy by using the iterated random function theory. A variant of the Ozarow-Leung code for the general two-user broadcast channel with feedback can be realized as a special case of our coding scheme. Furthermore, for the symmetric Gaussian broadcast channel with feedback, our coding scheme achieves the linear-feedback sum-capacity like the LQG code and outperforms the Kramer code.

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arXiv2016

Variable-to-Fixed Length Homophonic Coding with a Modified Shannon-Fano-Elias Code

Homophonic coding is a framework to reversibly convert a message into a sequence with some target distribution. This is a promising tool to generate a codeword with a biased code-symbol distribution, which is required for capacity-achieving communication by asymmetric channels. It is known that asymptotically optimal homophonic coding can be realized by a Fixed-to-Variable (FV) length code using an interval algorithm similar to a random number generator. However, FV codes are not preferable as a component of channel codes since a decoding error propagates to all subsequent codewords. As a solution for this problem an asymptotically optimal Variable-to-Fixed (VF) length homophonic code, dual Shannon-Fano-Elias-Gray (dual SFEG) code, is proposed in this paper. This code can be interpreted as a dual of a modified Shannon-Fano-Elias (SFE) code based on Gray code. It is also shown as a by-product that the modified SFE code, named SFEG code, achieves a better coding rate than the original SFE code in lossless source coding.

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arXiv2015

Almost Instantaneous Fix-to-Variable Length Codes

We propose almost instantaneous fixed-to-variable-length (AIFV) codes such that two (resp. $K-1$) code trees are used if code symbols are binary (resp. $K$-ary for $K \geq 3$), and source symbols are assigned to incomplete internal nodes in addition to leaves. Although the AIFV codes are not instantaneous codes, they are devised such that the decoding delay is at most two bits (resp. one code symbol) in the case of binary (resp. $K$-ary) code alphabet. The AIFV code can attain better average compression rate than the Huffman code at the expenses of a little decoding delay and a little large memory size to store multiple code trees. We also show for the binary and ternary AIFV codes that the optimal AIFV code can be obtained by solving 0-1 integer programming problems.

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arXiv2015

On the Capacity of Symmetric Gaussian Interference Channels with Feedback

In this paper, we propose a new coding scheme for symmetric Gaussian interference channels with feedback based on the ideas of time-varying coding schemes. The proposed scheme improves the Suh-Tse and Kramer inner bounds of the channel capacity for the cases of weak and not very strong interference. This improvement is more significant when the signal-to-noise ratio (SNR) is not very high. It is shown theoretically and numerically that our coding scheme can outperform the Kramer code. In addition, the generalized degrees-of-freedom of our proposed coding scheme is equal to the Suh-Tse scheme in the strong interference case. The numerical results show that our coding scheme can attain better performance than the Suh-Tse coding scheme for all channel parameters. Furthermore, the simplicity of the encoding/decoding algorithms is another strong point of our proposed coding scheme compared with the Suh-Tse coding scheme. More importantly, our results show that an optimal coding scheme for the symmetric Gaussian interference channels with feedback can be achieved by using only marginal posterior distributions under a better cooperation strategy between transmitters.

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arXiv2015

On Using Feedback in a Gaussian Channel

For information transmission a discrete time channel with independent additive Gaussian noise is used. There is also another channel with independent additive Gaussian noise (the feedback channel), and the transmitter observes without delay all outputs of the forward channel via that channel. Transmission of nonexponential number of messages is considered (i.e. transmission rate equals zero) and the achievable decoding error exponent for such a combination of channels is investigated. The transmission method strengthens the method used by authors earlier for BSC and Gaussian channels. In particular, for small feedback noise, it allows to gain 33.3\% (instead of 23.6\% earlier in the similar case of Gaussian channel).

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arXiv2014

Private Information Retrieval for Coded Storage

Private information retrieval scheme for coded data storage is considered in this paper. We focus on the case where the size of each data record is large and hence only the download cost (but not the upload cost for transmitting retrieval queries) is of interest. We prove that the tradeoff between storage cost and retrieval/download cost depends on the number of data records in the system. We also propose a fairly general class of linear storage codes and retrieval schemes and derive conditions under which our retrieval schemes are error-free and private. Tradeoffs between the storage cost and retrieval costs are also obtained. Finally, we consider special cases when the underlying storage code is based on an MDS code. Using our proposed method, we show that a randomly generated retrieval scheme is indeed very likely to be private and error-free.

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arXiv2014

Identification Codes to Identify Multiple Objects

In the case of ordinary identification coding, a code is devised to identify a single object among $N$ objects. But, in this paper, we consider an identification coding problem to identify $K$ objects at once among $N$ objects in the both cases that $K$ objects are ranked or not ranked. By combining Kurosawa-Yoshida scheme with Moulin-Koetter scheme, an efficient identification coding scheme is proposed, which can attain high coding rate and error exponents compared with the case that an ordinary identification code is used $K$ times. Furthermore, the achievable triplet of rate and error exponents of type I and type II decoding error probabilities are derived for the proposed coding scheme.

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arXiv2012

Coding Theorems for a (2,2)-Threshold Scheme with Detectability of Impersonation Attacks

In this paper, we discuss coding theorems on a $(2, 2)$--threshold scheme in the presence of an opponent who impersonates one of the two shareholders in an asymptotic setup. We consider a situation where $n$ secrets $S^n$ from a memoryless source is blockwisely encoded to two shares and the two shares are decoded to $S^n$ with permitting negligible decoding error. We introduce correlation level of the two shares and characterize the minimum attainable rates of the shares and a uniform random number for realizing a $(2, 2)$--threshold scheme that is secure against the impersonation attack by an opponent. It is shown that, if the correlation level between the two shares equals to an $\ell \ge 0$, the minimum attainable rates coincide with $H(S)+\ell$, where $H(S)$ denotes the entropy of the source, and the maximum attainable exponent of the success probability of the impersonation attack equals to $\ell$. We also give a simple construction of an encoder and a decoder using an ordinary $(2,2)$--threshold scheme where the two shares are correlated and attains all the bounds.

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arXiv2008

On zero-rate error exponent for BSC with noisy feedback

For the information transmission a binary symmetric channel is used. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all the outputs of the forward channel via that feedback channel. The transmission of a nonexponential number of messages (i.e. the transmission rate equals zero) is considered. The achievable decoding error exponent for such a combination of channels is investigated. It is shown that if the crossover probability of the feedback channel is less than a certain positive value, then the achievable error exponent is better than the similar error exponent of the no-feedback channel. The transmission method described and the corresponding lower bound for the error exponent can be strengthened, and also extended to the positive transmission rates.

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arXiv2005

Secure multiplex coding to attain the channel capacity in wiretap channels

It is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so-called secrecy capacity $C_S$, which is usually smaller than the channel capacity $C$. In order to remove the loss $C - C_S$, we propose a multiplex coding scheme with plural independent messages. In this paper, it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each message. The coding theorem is proved by extending Hayashi's proof, in which the coding of the channel resolvability is applied to wiretap channels.

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arXiv2005

Asymptotically Optimal Tree-based Group Key Management Schemes

In key management schemes that realize secure multicast communications encrypted by group keys on a public network, tree structures are often used to update the group keys efficiently. Selcuk and Sidhu have proposed an efficient scheme which updates dynamically the tree structures based on the withdrawal probabilities of members. In this paper, it is shown that Selcuk-Sidhu scheme is asymptotically optimal for the cost of withdrawal. Furthermore, a new key management scheme, which takes account of key update costs of joining in addition to withdrawal, is proposed. It is proved that the proposed scheme is also asymptotically optimal, and it is shown by simulation that it can attain good performance for nonasymptotic cases.

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