Papers by Toshiyuki Tanaka
2009 IEEE International Symposium on Information Theory, 2009
Channel polarization is a method of constructing capacity achieving codes for symmetric binary-in... more Channel polarization is a method of constructing capacity achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this paper, a new construction method for arbitrary symmetric binary memoryless channel (B-MC) with linear complexity in the blocklength is proposed. Furthermore, new upper bound and lower bound of the block error probability of polar codes are derived for the BEC and arbitrary symmetric B-MC, respectively.
2010 IEEE Information Theory Workshop, 2010
Polar codes, introduced by Arıkan, achieve symmetric capacity of any discrete memoryless channels... more Polar codes, introduced by Arıkan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error probability of non-binary polar codes constructed on the basis of Reed-Solomon matrices by numerical simulations. It is confirmed that 4-ary polar codes have significantly better performance than binary polar codes on binary-input AWGN channel. We also discuss an interpretation of polar codes in terms of algebraic geometry codes, and further show that polar codes using Hermitian codes have asymptotically good performance.
2010 IEEE International Symposium on Information Theory, 2010
A rate-dependent upper bound of the best achievable block error probability of polar codes with s... more A rate-dependent upper bound of the best achievable block error probability of polar codes with successivecancellation decoding is derived.
IEEE Transactions on Knowledge and Data Engineering, 2011
We propose a framework for improving classifier performance by effectively using auxiliary sample... more We propose a framework for improving classifier performance by effectively using auxiliary samples. The auxiliary samples are labeled not in terms of the target taxonomy according to which we wish to classify samples, but according to classification schemes or taxonomies that are different from the target taxonomy. Our method finds a classifier by minimizing a weighted error over the target and auxiliary samples. The weights are defined so that the weighted error approximates the expected error when samples are classified into the target taxonomy. Experiments using synthetic and text data show that our method significantly improves the classifier performance in most cases compared to conventional data augmentation methods.
IEEE Transactions on Information Theory, 2013
For a binary-input memoryless symmetric channel W , we consider the asymptotic behavior of the po... more For a binary-input memoryless symmetric channel W , we consider the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over W . In particular, we study the asymptotics of the cumulative distribution P(Zn ≤ z), where {Zn} is the Bhattacharyya process defined from W , and its dependence on the rate of transmission. On the basis of this result, we characterize the asymptotic behavior, as well as its dependence on the rate, of the block error probability of polar codes using the successive cancellation decoder. This refines the original bounds by Arıkan and Telatar. Our results apply to general polar codes based on ℓ × ℓ kernel matrices. We also provide lower bounds on the block error probability of polar codes using the MAP decoder. The MAP lower bound and the successive cancellation upper bound coincide when ℓ = 2, but there is a gap for ℓ > 2. Polar codes, introduced by Arıkan [1], are a family of codes that provably achieve the capacity of binary-input memoryless symmetric (BMS) channels using low-complexity encoding and decoding algorithms. Since their invention, there has been a large body of work that has analyzed (see e.g., [2]- ) and extended (see e.g., [12] -[20]) these codes. The construction of polar codes is based on an ℓ × ℓ matrix G, with entries in {0, 1}, called the kernel matrix. Besides being invertible, the matrix G should have the property that none of its column permutations is upper triangular . We call a matrix G with such properties a polarizing matrix and in the following, whenever we speak of a kernel matrix G, we assume that G is polarizing.
IEEE Transactions on Information Theory, 2013
We consider communication over the binary erasure channel (BEC) using low-density parity-check (L... more We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding. For fixed numbers of BP iterations, the bit error probability approaches a limit as blocklength tends to infinity, and the limit is obtained via density evolution. On the other hand, the difference between the bit error probability of codes with blocklength n and that in the large blocklength limit is asymptotically α(ǫ, t)/n + Θ(n −2) where α(ǫ, t) denotes a specific constant determined by the code ensemble considered, the number t of iterations, and the erasure probability ǫ of the BEC. In this paper, we derive a set of recursive formulas which allows evaluation of the constant α(ǫ, t) for standard irregular ensembles. The dominant difference α(ǫ, t)/n can be considered as effects of cycle-free and singlecycle structures of local graphs. Furthermore, it is confirmed via numerical simulations that estimation of the bit error probability using α(ǫ, t) is accurate even for small blocklengths.
We analyze the bit error probability of multiuser demodulators for directsequence binary phase-sh... more We analyze the bit error probability of multiuser demodulators for directsequence binary phase-shift-keying (DS/BPSK) CDMA channel with additive gaussian noise. The problem of multiuser demodulation is cast into the finite-temperature decoding problem, and replica analysis is applied to evaluate the performance of the resulting MPM (Marginal Posterior Mode) demodulators, which include the optimal demodulator and the MAP demodulator as special cases. An approximate implementation of demodulators is proposed using analog-valued Hopfield model as a naive mean-field approximation to the MPM demodulators, and its performance is also evaluated by the replica analysis. Results of the performance evaluation shows effectiveness of the optimal demodulator and the mean-field demodulator compared with the conventional one, especially in the cases of small information bit rate and low noise level.
2008 6th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks and Workshops
Statistical mechanics-based approach to studying wireless communication systems is useful not onl... more Statistical mechanics-based approach to studying wireless communication systems is useful not only in analyzing theoretical performance of a given model, but also in optimizing design of a class of system models. In this paper, we demonstrate usefulness of statistical-mechanics approach in the problem of optimizing a spreading sequence set of randomly-spread codedivision multiple-access (CDMA) communication systems. It has been shown that the optimal spreading sequences of a randomly spread CDMA channel in the large-system limit are Welchbound-equality sequence sets, even when a non-Gaussian input distribution is assumed.
IEEJ Transactions on Fundamentals and Materials
Information Geometry of Mean Field Approximation
Neco, 1999
I present a general theory of mean-field approximation based on information geometry and applicab... more I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the “naive” mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics.
Information Geometry of Turbo Code And Gallager Code
Active noise control system in a duct with reflection at both ends (No. 3)
Active noise control system in a duct with reflection at both terminals
Analysis on induced electric field within eccentric multilayered sphere assuming membrane structure
The Bethe approximation, discovered in statistical physics, gives an efficient algorithm called b... more The Bethe approximation, discovered in statistical physics, gives an efficient algorithm called belief propagation (BP) for approximating a partition function. BP empirically gives an accurate approximation for many problems, e.g., low-density parity-check codes, compressed sensing, etc. Recently, Vontobel gives a novel characterization of the Bethe approximation using graph cover. In this paper, a new approximation based on the Bethe approximation is proposed. The new approximation is derived from Vontobel's characterization using graph cover, and expressed by using the edge zeta function, which is related with the Hessian of the Bethe free energy as shown by Watanabe and Fukumizu. On some conditions, it is proved that the new approximation is asymptotically better than the Bethe approximation.
Approximate Theory for Dynamics of DS-CDMA Multistage Detector
J. Phys. Conf. Ser. 95: International Workshop on Statistical-Mechanical Informatics 2007
Adaptive Active Noise Control in a Duct using Two Reference Sensors in Consideration of the Reflecti
Ieee International Symposium on Information Theory 2003 Proceedings, Jul 4, 2003
Japan e-mail: tandca(0eei .metro-u.ac. j p IEEE h n s. In. Theory, 2002.
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Papers by Toshiyuki Tanaka