Channel Coding and Lossy Source Coding Using a Constrained Random Number Generator

Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code are finite. Random numbers, which satisfy a condition specified by a function and its value, are used to construct stochastic encoders. The proof of the theorems is based on the hash property of an ensemble of functions, where the results are extended to general channels/sources and alternative formulas are introduced for channel capacity and the rate-distortion region. Since an ensemble of sparse matrices has a hash property, we can construct a code by using sparse matrices, where the sum-product algorithm can be used for encoding and decoding by assuming that channels/sources are memoryless.Comment: submitted to IEEE Transactions on Information Theory, 42 page

Construction of Codes for Wiretap Channel and Secret Key Agreement from Correlated Source Outputs by Using Sparse Matrices

The aim of this paper is to prove coding theorems for the wiretap channel coding problem and secret key agreement problem based on the the notion of a hash property for an ensemble of functions. These theorems imply that codes using sparse matrices can achieve the optimal rate. Furthermore, fixed-rate universal coding theorems for a wiretap channel and a secret key agreement are also proved.Comment: A part of this paper is presented in part at 2009 IEEE Information Theory Workshop (ITW2009), Taormina, Italy, pp.105-109, 2009. This paper is submitted to IEEE Transactions on Information Theory. 34 page

Construction of Multiple Access Channel Codes Based on Hash Property

The aim of this paper is to introduce the construction of codes for a general discrete stationary memoryless multiple access channel based on the the notion of the hash property. Since an ensemble of sparse matrices has a hash property, we can use sparse matrices for code construction. Our approach has a potential advantage compared to the conventional random coding because it is expected that we can use some approximation algorithms by using the sparse structure of codes.Comment: This paper has been presented in part at Proc. 2011 IEEE Internal Symposium on Information Theory and submitted to IEEE Transactions on Information Theory. 39 page

Construction of Slepian-Wolf Source Code and Broadcast Channel Code Based on Hash Property

The aim of this paper is to prove theorems for the Slepian-Wolf source coding and the broadcast channel coding (independent messages and no common message) based on the the notion of a stronger version of the hash property for an ensemble of functions. Since an ensemble of sparse matrices has a strong hash property, codes using sparse matrices can realize the achievable rate region. Furthermore, extensions to the multiple source coding and multiple output broadcast channel coding are investigated.Comment: The proofs of Lemmas 4 and 9 are revised. Some proofs are simplified. Some typos are fixed. A part of this paper has been published in Proceedings of 2010 IEEE International Symposium on Information Theory (ISIT2010) and Proceedings of 7th Asia-Europe Workshop "CONCEPTS in INFORMATION THEORY" (AEW7), 2011, 39 page

Finite-Block-Length Analysis in Classical and Quantum Information Theory

Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects

Quantum wiretap channel with non-uniform random number and its exponent and equivocation rate of leaked information

A usual code for quantum wiretap channel requires an auxiliary random variable subject to the perfect uniform distribution. However, it is difficult to prepare such an auxiliary random variable. We propose a code that requires only an auxiliary random variable subject to a non-uniform distribution instead of the perfect uniform distribution. Further, we evaluate the exponential decreasing rate of leaked information and derive its equivocation rate. For practical constructions, we also discuss the security when our code consists of a linear error correcting code