Tetsunao Matsuta

Universal Slepian-Wolf source codes using low-density parity-check matrices

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.

Revisiting the Slepian-Wolf coding problem for general sources: A direct approach

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.

Revisiting the rate-distortion theory using smooth max Rényi divergence

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.

Non-asymptotic bounds for fixed-length lossy compression

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.

A general formula of rate-distortion functions for source coding with side information at many decoders

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.

Source coding with side information at the decoder revisited

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 Warsis result. Then, combining these results, we clarify the ε-achievable rate region of the WAK coding system.

Achievable rate regions for asynchronous Slepian-Wolf coding systems

The Slepian-Wolf (SW) coding system is a source coding system with two encoders and a decoder, where these encoders independently encode input sequences emitted from two correlated sources into fixed-length codewords, and the decoder reconstructs all input sequences from the codewords. In this paper, we consider the situation in which the SW coding system is asynchronous, i.e., each encoder runs with each delay from the base time. We assume that these delays are unknown to encoders and a decoder, but the maximum of delays is known to encoders and the decoder. For this asynchronous SW coding system, we clarify 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 show an exponential bound of the error probability for this coding system by using Gallagers random coding techniques.

Rate-distortion functions for source coding when side information with unknown delay may be present

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.

A general formula for capacity of channels with action-dependent states

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.

Closed forms of the achievable rate region for Wyner's source coding systems

Wyners 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 Wyners source coding system.