A spatially “Mt. Fuji” coupled (SFC) low-density parity-check (LDPC) ensemble is a modified version of the spatially coupled (SC) LDPC ensemble. Its decoding error probability in the waterfall region has been studied only in an experimental manner. In this paper, we theoretically analyze it over the binary erasure channel by modifying the expected graph evolution (EGE) and covariance evolution (CE) that have been used to analyze the original SC-LDPC ensemble. In particular, we derive the initial condition modified for the SFC-LDPC ensemble. Then, unlike the SC-LDPC ensemble, the SFC-LDPC ensemble has a local minimum on the solution of the EGE and CE. Considering the property of it, we theoretically expect the waterfall curve of the SFC-LDPC ensemble is steeper than that of the SC-LDPC ensemble. In addition, we also confirm it by numerical experiments.

In a practical classification problem, there are cases where incorrect labels are included in training data due to label noise. We introduce a classification method in the presence of label noise that idealizes a classification method based on the expectation-maximization (EM) algorithm, and evaluate its performance theoretically. Its performance is asymptotically evaluated by assessing the risk function defined as the Kullback-Leibler divergence between predictive distribution and true distribution. The result of this performance evaluation enables a theoretical evaluation of the most successful performance that the EM-based classification method may achieve.

The context tree model has the property that the occurrence probability of symbols is determined from a finite past sequence and is a broader class of sources that includes i.i.d. or Markov sources. This paper proposes a non-stationary source with context tree models that change from interval to interval. The Bayes code for this source requires weighting of the posterior probabilities of the context tree models and change points, so the computational complexity of it usually increases to exponential order. Therefore, the challenge is how to reduce the computational complexity. In this paper, we propose a special class of prior probability distribution of context tree models and change points and develop an efficient Bayes coding algorithm by combining two existing Bayes coding algorithms. The algorithm minimizes the Bayes risk function of the proposed source in this paper, and the computational complexity of the proposed algorithm is polynomial order. We investigate the behavior and performance of the proposed algorithm by conducting experiments.

Previously, we proposed a probabilistic data generation model represented by an unobservable tree and a sequential updating method to calculate a posterior distribution over a set of trees. The set is called a meta-tree. In this paper, we propose a more efficient batch updating method.

We analyze the extended stochastic complexity (ESC) which has been proposed by K. Yamanishi. The ESC can be applied to learning algorithms for on-line prediction and batch-learning settings. Yamanishi derived the upper bound of ESC satisfying uniformly for all data sequences and that of the asymptotic expectation of ESC. However, Yamanishi concentrates mainly on the worst case performance and the lower bound has not been derived. In this paper, we show some interesting properties of ESC which are similar to Bayesian statistics: the Bayes rule and the asymptotic normality. We then derive the asymptotic formula of ESC in the meaning of almost sure and mean convergence within an error of o(1) using these properties.

We treat lossless fixed-to-variable length source coding under general sources for finite block length setting. We evaluate the threshold of the overflow probability for prefix and non-prefix codes in terms of the smooth max-entropy. We clarify the difference of the thresholds between prefix and non-prefix codes for finite block length. Further, we discuss our results under the asymptotic block length setting.

In this paper, we develop linear-programming (LP) decoding for multiple-access channels with binary linear codes. For single-user channels, LP decoding has attracted much attention in recent years as a good approximation to maximum-likelihood (ML) decoding. We demonstrate how the ML decoding problem for multiple-access channels with binary linear codes can be formulated as an LP problem. This is not straightforward, because the objective function of the problem is generally a non-linear function of the codeword symbols. We introduce auxiliary variables such that the objective function is a linear function of these variables. The ML decoding problem then reduces to the LP problem. As in the case for single-user channels, we formulate the relaxed LP problem to reduce the complexity for practical implementation, and as a result propose a decoder that has the desirable property known as the ML certificate property (i.e., if the decoder outputs an integer solution, the solution is guaranteed to be the ML codeword). Although the computational complexity of the proposed algorithm is exponential in the number of users, we can reduce this complexity for Gaussian multiple-access channels. Furthermore, we compare the performance of the proposed decoder with a decoder based on the sum-product algorithm.

This paper presents MACs that combine a block cipher and its component such as a reduced-round version. Our MACs are faster than the standard MAC modes such as CBC-MAC, and provably secure if the block cipher is pseudorandom and its component is a permutation with a small differential probability. Such a MAC scheme was recently proposed by one of authors, and we provide improvements about security and treading-off between speed and amount of preprocessing.