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Tadashi Wadayama

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Published work

29 published item(s)

preprint2026arXiv

Federated Learning with Hypergradient-based Online Update of Aggregation Weights

Federated learning using mobile and Internet of Things devices requires not only the ability to handle heterogeneity of clients' data distributions but also high adaptability to varying communication environments. We propose FedHAW (Federated Learning with Hypergradient-based update of Aggregation Weights) that implements online updates of aggregation weights. FedHAW updates the aggregation weights by using hypergradient, the gradient of the objective function with respect to the weights, which can be calculated with low computational overhead. Simulation results show that the proposed method possesses high generalization performance in heterogeneous environments and high robustness to communication errors.

preprint2026arXiv

Information Gradient for Directed Acyclic Graphs: A Score-based Framework for End-to-End Mutual Information Maximization

This paper presents a general framework for end-to-end mutual information maximization in communication and sensing systems represented by stochastic directed acyclic graphs (DAGs). We derive a unified formula for the (mutual) information gradient with respect to arbitrary internal parameters, utilizing marginal and conditional score functions. We demonstrate that this gradient can be efficiently computed using vector-Jacobian products (VJP) within standard automatic differentiation frameworks, enabling the optimization of complex networks under global resource constraints. Numerical experiments on both linear multipath DAGs and nonlinear channels validate the proposed framework; the results confirm that the estimator, utilizing score functions learned via denoising score matching, accurately reproduces ground-truth gradients and successfully maximizes end-to-end mutual information. Beyond maximization, we extend our score-based framework to a novel unsupervised paradigm: digital twin calibration via Fisher divergence minimization.

preprint2026arXiv

Mutual Information Estimation via Score-to-Fisher Bridge for Nonlinear Gaussian Noise Channels

We present a numerical method to evaluate mutual information (MI) in nonlinear Gaussian noise channels by using denoising score matching (DSM) learning for estimating the score function of channel output. Via de Bruijn's identity, Fisher information estimated from the learned score function yields accurate estimates of MI through a Fisher integral representation for a variety of priors and channel nonlinearities. In this work, we propose a comprehensive theoretical foundation for the Score-to-Fisher bridge methodology, along with practical guidelines for its implementation. We also conduct extensive validation experiments, comparing our approach with closed-form solutions and a kernel density estimation baseline. The results of our numerical experiments demonstrate that the proposed method is both practical and efficient for MI estimation in nonlinear Gaussian noise channels. Additionally, we discuss the theoretical connections between our score-based framework and thermodynamic concepts, such as partition function estimation and optimal transport.

preprint2026arXiv

Score-Based VAMP with Fisher-Information-Based Onsager Correction

We propose score-based VAMP (SC-VAMP), a variant of vector approximate message passing (VAMP) in which the Onsager correction is expressed and computed via conditional Fisher information, thereby enabling a Jacobian-free implementation. Using learned score functions, SC-VAMP constructs nonlinear MMSE estimators through Tweedie's formula and derives the corresponding Onsager terms from the score-norm statistics, avoiding the need for analytical derivatives of the prior or likelihood. When combined with random orthogonal/unitary mixing to mitigate non-ideal, structured or correlated sensing settings, the proposed framework extends VAMP to complex black-box inference problems where explicit modeling is intractable. Finally, by leveraging the entropic CLT, we provide an information-theoretic perspective on the Gaussian approximation underlying SE, offering insight into the decoupling principle beyond idealized i.i.d. settings, including nonlinear regimes.

preprint2022arXiv

MMSE Signal Detection for MIMO Systems based on Ordinary Differential Equation

Motivated by emerging technologies for energy efficient analog computing and continuous-time processing, this paper proposes continuous-time minimum mean squared error estimation for multiple-input multiple-output (MIMO) systems based on an ordinary differential equation. Mean squared error (MSE) is a principal detection performance measure of estimation methods for MIMO systems. We derive an analytical MSE formula that indicates the MSE at any time. The MSE of the proposed method depends on a regularization parameter which affects the convergence property of the MSE. Furthermore, we extend the proposed method by using a time-dependent regularization parameter to achieve better convergence performance. Numerical experiments indicated excellent agreement with the theoretical values and improvement in the convergence performance owing to the use of the time-dependent parameter.

preprint2022arXiv

Precoder Design for Correlated Data Aggregation via Over-the-Air Computation in Sensor Networks

Over-the-air computation (AirComp) enables efficient wireless data aggregation in sensor networks by simultaneous processing of calculation and communication. This paper proposes a novel precoder design for AirComp that incorporates statistical properties of sensing data, spatial correlation and heterogeneous data correlation. The proposed design of the precoder requires no iterative processes so that it can be realized with low computational costs. Moreover, this method provides dimensionality reduction of sensing data to reduce communication costs per sensor. We evaluate performance of the proposed method in terms of various system parameters. The results show the superiority of the proposed method to conventional non-iterative methods in cases where there are a large number of sensors and where the number of receive antennas at the aggregator is less than that of the total transmit antennas at the sensors.

preprint2021arXiv

Proximal Decoding for LDPC-coded Massive MIMO Channels

We propose a novel optimization-based decoding algorithm for LDPC-coded massive MIMO channels. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem. The key idea is the use of a code-constraint polynomial penalizing a vector far from a codeword as a regularizer in the approximate MAP objective function. The code proximal operator is naturally derived from code-constraint polynomials. The proposed algorithm, called proximal decoding, can be described by a simple recursion consisting of the gradient descent step for a negative log-likelihood function and the code proximal operation. Several numerical experiments show that the proposed algorithm outperforms known massive MIMO detection algorithms, such as an MMSE detector with belief propagation decoding.

preprint2020arXiv

Chebyshev Inertial Landweber Algorithm for Linear Inverse Problems

The Landweber algorithm defined on complex/real Hilbert spaces is a gradient descent algorithm for linear inverse problems. Our contribution is to present a novel method for accelerating convergence of the Landweber algorithm. In this paper, we first extend the theory of the Chebyshev inertial iteration to the Landweber algorithm on Hilbert spaces. An upper bound on the convergence rate clarifies the speed of global convergence of the proposed method. The Chebyshev inertial Landweber algorithm can be applied to wide class of signal recovery problems on a Hilbert space including deconvolution for continuous signals. The theoretical discussion developed in this paper naturally leads to a novel practical signal recovery algorithm. As a demonstration, a MIMO detection algorithm based on the projected Landweber algorithm is derived. The proposed MIMO detection algorithm achieves much smaller symbol error rate compared with the MMSE detector.

preprint2020arXiv

Deep Unfolded Multicast Beamforming

Multicast beamforming is a promising technique for multicast communication. Providing an efficient and powerful beamforming design algorithm is a crucial issue because multicast beamforming problems such as a max-min-fair problem are NP-hard in general. Recently, deep learning-based approaches have been proposed for beamforming design. Although these approaches using deep neural networks exhibit reasonable performance gain compared with conventional optimization-based algorithms, their scalability is an emerging problem for large systems in which beamforming design becomes a more demanding task. In this paper, we propose a novel deep unfolded trainable beamforming design with high scalability and efficiency. The algorithm is designed by expanding the recursive structure of an existing algorithm based on projections onto convex sets and embedding a constant number of trainable parameters to the expanded network, which leads to a scalable and stable training process. Numerical results show that the proposed algorithm can accelerate its convergence speed by using unsupervised learning, which is a challenging training process for deep unfolding.

preprint2020arXiv

Theoretical Interpretation of Learned Step Size in Deep-Unfolded Gradient Descent

Deep unfolding is a promising deep-learning technique in which an iterative algorithm is unrolled to a deep network architecture with trainable parameters. In the case of gradient descent algorithms, as a result of the training process, one often observes the acceleration of the convergence speed with learned non-constant step size parameters whose behavior is not intuitive nor interpretable from conventional theory. In this paper, we provide a theoretical interpretation of the learned step size of deep-unfolded gradient descent (DUGD). We first prove that the training process of DUGD reduces not only the mean squared error loss but also the spectral radius related to the convergence rate. Next, we show that minimizing the upper bound of the spectral radius naturally leads to the Chebyshev step which is a sequence of the step size based on Chebyshev polynomials. The numerical experiments confirm that the Chebyshev steps qualitatively reproduce the learned step size parameters in DUGD, which provides a plausible interpretation of the learned parameters. Additionally, we show that the Chebyshev steps achieve the lower bound of the convergence rate for the first-order method in a specific limit without learning parameters or momentum terms.

preprint2016arXiv

Bounds on Asymptotic Rate of Capacitive Crosstalk Avoidance Codes for On-chip Buses

In order to prevent the capacitive crosstalk in on-chip buses, several types of capacitive crosstalk avoidance codes have been devised. These codes are designed to prohibit transition patterns prone to the capacity crosstalk from any consecutive two words transmitted to on-chip buses. This paper provides a rigorous analysis on the asymptotic rate of (p,q)-transition free word sequences under the assumption that coding is based on a pair of a stateful encoder and a stateless decoder. The symbols p and q represent k-bit transition patterns that should not be appeared in any consecutive two words at the same adjacent k-bit positions. It is proved that the maximum rate of the sequences equals to the subgraph domatic number of (p,q)-transition free graph. Based on the theoretical results on the subgraph domatic partition problem, a pair of lower and upper bounds on the asymptotic rate is derived. We also present that the asymptotic rate 0.8325 is achievable for the (10,01)-transition free word sequences.

preprint2016arXiv

Performance Analysis based on Density Evolution on Fault Erasure Belief Propagation Decoder

In this paper, we will present an analysis on the fault erasure BP decoders based on the density evolution. In the fault BP decoder, messages exchanged in a BP process are stochastically corrupted due to unreliable logic gates and flip-flops; i.e., we assume circuit components with transient faults. We derived a set of the density evolution equations for the fault erasure BP processes. Our density evolution analysis reveals the asymptotic behaviors of the estimation error probability of the fault erasure BP decoders. In contrast to the fault free cases, it is observed that the error probabilities of the fault erasure BP decoder converge to positive values, and that there exists a discontinuity in an error curve corresponding to the fault BP threshold. It is also shown that an message encoding technique provides higher fault BP thresholds than those of the original decoders at the cost of increased circuit size.

preprint2016arXiv

Sparse Signal Recovery for Binary Compressed Sensing by Majority Voting Neural Networks

In this paper, we propose majority voting neural networks for sparse signal recovery in binary compressed sensing. The majority voting neural network is composed of several independently trained feedforward neural networks employing the sigmoid function as an activation function. Our empirical study shows that a choice of a loss function used in training processes for the network is of prime importance. We found a loss function suitable for sparse signal recovery, which includes a cross entropy-like term and an $L_1$ regularized term. From the experimental results, we observed that the majority voting neural network achieves excellent recovery performance, which is approaching the optimal performance as the number of component nets grows. The simple architecture of the majority voting neural networks would be beneficial for both software and hardware implementations.

preprint2015arXiv

Band Splitting Permutations for Spatially Coupled LDPC Codes Enhancing Burst Erasure Immunity

It is well known that spatially coupled (SC) codes with erasure-BP decoding have powerful error correcting capability over memoryless erasure channels. However, the decoding performance of SC-codes significantly degrades when they are used over burst erasure channels. In this paper, we propose band splitting permutations (BSP) suitable for $(l,r,L)$ SC-codes. The BSP splits a diagonal band in a base matrix into multiple bands in order to enhance the span of the stopping sets in the base matrix. As theoretical performance guarantees, lower and upper bounds on the maximal burst correctable length of the permuted $(l,r,L)$ SC-codes are presented. Those bounds indicate that the maximal correctable burst ratio of the permuted SC-codes converges to 1/k where k=r/l. This implies the asymptotic optimality of the permuted SC-codes in terms of burst erasure correction.

preprint2015arXiv

Evaluation of Symmetric Mutual Information of the Simplified TDMR Channel Model

In the present paper, a simplified two-dimensional magnetic recording (TDMR) channel model is proposed in order to capture the qualitative features of writing and read-back processes of TDMR systems.The proposed channel model incorporates the effects of both linear interference from adjacent bit-cells and signal-dependent noise due to irregular grain boundaries between adjacent bit-cells. The simplicity of the proposed model enables us to derive the closed form of the conditional PDF representing the probabilistic nature of the channel. The conditional PDF is Gaussian distributed and is parameterized by a signal-dependent covariance matrix. Based on this conditional PDF, a Monte Carlo method for approximating the symmetric mutual information of this channel is developed. The symmetric mutual information is closely related to the areal density limit for TDMR systems. The numerical results suggest that we may need low-rate coding, e.g., 2/3 or 1/2, when the jitter-like noise becomes dominant.

preprint2015arXiv

Index ARQ Protocol for Reliable Contents Distribution over Broadcast Channels

In the present paper, we propose a broadcast ARQ protocol based on the concept of index coding. In the proposed scenario, a server wishes to transmit a finite sequence of packets to multiple receivers via a broadcast channel with packet erasures until all of the receivers successfully receive all of the packets. In the retransmission phase, the server produces a coded packet as a retransmitted packet based on the side-information sent from the receivers via feedback channels. A notable feature of the proposed protocol is that the decoding process at the receiver side has low decoding complexity because only a small number of addition operations are needed in order to recover an intended packet. This feature may be preferable for reducing the power consumption of receivers. The throughput performance of the proposed protocol is close to that of the ideal FEC throughput performance when the erasure probability is less than $0.1$. This implies that the proposed protocol provides almost optimal throughput performance in such a regime.

preprint2015arXiv

Subgraph Domatic Problem and Writing Capacity of Memory Devises with Restricted State Transitions

A code design problem for memory devises with restricted state transitions is formulated as a combinatorial optimization problem that is called a subgraph domatic partition (subDP) problem. If any neighbor set of a given state transition graph contains all the colors, then the coloring is said to be valid. The goal of a subDP problem is to find a valid coloring with the largest number of colors for a subgraph of a given directed graph. The number of colors in an optimal valid coloring gives the writing capacity of a given state transition graph. The subDP problems are computationally hard; it is proved to be NP-complete in this paper. One of our main contributions in this paper is to show the asymptotic behavior of the writing capacity $C(G)$ for sequences of dense bidirectional graphs, that is given by C(G)=Omega(n/ln n) where n is the number of nodes. A probabilistic method called Lovasz local lemma (LLL) plays an essential role to derive the asymptotic expression.

preprint2014arXiv

Bitwise MAP Algorithm for Group Testing based on Holographic Transformation

In this paper, an exact bitwise MAP (Maximum A Posteriori) estimation algorithm for group testing problems is presented. We assume a simplest non-adaptive group testing scenario including N-objects with binary status and M-disjunctive tests. If a group contains a positive object, the test result for the group is assumed to be one; otherwise, the test result becomes zero. Our inference problem is to evaluate the posterior probabilities of the objects from the observation of M-test results and from our knowledge on the prior probabilities for objects. The heart of the algorithm is the dual expression of the posterior values. The derivation of the dual expression can be naturally described based on a holographic transformation to the normal factor graph (NFG) representing the inference problem.

preprint2013arXiv

An Analysis on Minimum s-t Cut Capacity of Random Graphs with Specified Degree Distribution

The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not so trivial to predict statistical properties on the maximum flow of the network. In this paper, we present a probabilistic analysis for evaluating the accumulate distribution of the minimum s-t cut capacity on random graphs. The graph ensemble treated in this paper consists of weighted graphs with arbitrary specified degree distribution. The main contribution of our work is a lower bound for the accumulate distribution of the minimum s-t cut capacity. From some computer experiments, it is observed that the lower bound derived here reflects the actual statistical behavior of the minimum s-t cut capacity of random graphs with specified degrees.

preprint2013arXiv

Finite Length Analysis on Listing Failure Probability of Invertible Bloom Lookup Tables

The Invertible Bloom Lookup Tables (IBLT) is a data structure which supports insertion, deletion, retrieval and listing operations of the key-value pair. The IBLT can be used to realize efficient set reconciliation for database synchronization. The most notable feature of the IBLT is the complete listing operation of the key-value pairs based on the algorithm similar to the peeling algorithm for low-density generator-matrix (LDGM) codes. In this paper, we will present a stopping set (SS) analysis for the IBLT which reveals finite length behaviors of the listing failure probability. The key of the analysis is enumeration of the number of stopping matrices of given size. We derived a novel recursive formula useful for computationally efficient enumeration. An upper bound on the listing failure probability based on the union bound accurately captures the error floor behaviors. It will be shown that, in the error floor region, the dominant SS have size 2. We propose a simple modification on hash functions, which are called SS avoiding hash functions, for preventing occurrences of the SS of size 2.

preprint2013arXiv

Non-Adaptive Group Testing based on Sparse Pooling Graphs

In this paper, an information theoretic analysis on non-adaptive group testing schemes based on sparse pooling graphs is presented. The binary status of the objects to be tested are modeled by i.i.d. Bernoulli random variables with probability p. An (l, r, n)-regular pooling graph is a bipartite graph with left node degree l and right node degree r, where n is the number of left nodes. Two scenarios are considered: a noiseless setting and a noisy one. The main contributions of this paper are direct part theorems that give conditions for the existence of an estimator achieving arbitrary small estimation error probability. The direct part theorems are proved by averaging an upper bound on estimation error probability of the typical set estimator over an (l,r, n)-regular pooling graph ensemble. Numerical results indicate sharp threshold behaviors in the asymptotic regime.

preprint2012arXiv

A Coding Theoretic Approach for Evaluating Accumulate Distribution on Minimum Cut Capacity of Weighted Random Graphs

The multicast capacity of a directed network is closely related to the $s$-$t$ maximum flow, which is equal to the $s$-$t$ minimum cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or have stochastic nature, it is not so trivial to predict statistical properties on the maximum flow. In this paper, we present a coding theoretic approach for evaluating the accumulate distribution of the minimum cut capacity of weighted random graphs. The main feature of our approach is to utilize the correspondence between the cut space of a graph and a binary LDGM (low-density generator-matrix) code with column weight 2. The graph ensemble treated in the paper is a weighted version of Erdős-Rényi random graph ensemble. The main contribution of our work is a combinatorial lower bound for the accumulate distribution of the minimum cut capacity. From some computer experiments, it is observed that the lower bound derived here reflects the actual statistical behavior of the minimum cut capacity.

preprint2012arXiv

A New Direction for Counting Perfect Matchings

In this paper, we present a new exact algorithm for counting perfect matchings, which relies on neither inclusion-exclusion principle nor tree-decompositions. For any bipartite graph of $2n$ nodes and $Δn$ edges such that $Δ\geq 3$, our algorithm runs with $O^{\ast}(2^{(1 - 1/O(Δ\log Δ))n})$ time and exponential space. Compared to the previous algorithms, it achieves a better time bound in the sense that the performance degradation to the increase of $Δ$ is quite slower. The main idea of our algorithm is a new reduction to the problem of computing the cut-weight distribution of the input graph. The primary ingredient of this reduction is MacWilliams Identity derived from elementary coding theory. The whole of our algorithm is designed by combining that reduction with a non-trivial fast algorithm computing the cut-weight distribution. To the best of our knowledge, the approach posed in this paper is new and may be of independent interest.

preprint2011arXiv

A signal recovery algorithm for sparse matrix based compressed sensing

We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest that the developed algorithm saturates the Donoho-Tanner weak threshold for the perfect recovery when the matrix becomes as dense as the signal size $N$ and the number of measurements $M$ tends to infinity keep $α=M/N \sim O(1)$, which is supported by extensive numerical experiments. Even when the numbers of non-zero entries per column/row in the measurement matrices are limited to $O(1)$, numerical experiments indicate that the algorithm can still typically recover the original signal perfectly with an $O(N)$ computational cost per update as well if the density $ρ$ of non-zero entries of the signal is lower than a certain critical value $ρ_{\rm th}(α)$ as $N,M \to \infty$.

preprint2011arXiv

Layered Index-less Indexed Flash Codes for Improving Average Performance

In the present paper, a modification of the Index-less Indexed Flash Codes (ILIFC) for flash memory storage system is presented. Although the ILIFC proposed by Mahdavifar et al. has excellent worst case performance, the ILIFC can be further improved in terms of the average case performance. The proposed scheme, referred to as the {\em layered ILIFC}, is based on the ILIFC. However, the primary focus of the present study is the average case performance. The main feature of the proposed scheme is the use of the layer-based index coding to represent indices of information bits. The layer index coding promotes the uniform use of cell levels, which leads to better average case performance. Based on experiments, the proposed scheme achieves a larger average number of rewritings than the original ILIFC without loss of worst case performance.

preprint2011arXiv

LP Decodable Permutation Codes based on Linearly Constrained Permutation Matrices

A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding problem for the proposed class of permutation codes as a linear programming (LP) problem. The main feature of this class of permutation codes, called LP decodable permutation codes, is this LP decodability. It is demonstrated that the LP decoding performance of the proposed class of permutation codes is characterized by the vertices of the code polytope of the code. Two types of linear constraints are discussed; one is structured constraints and another is random constraints. The structured constraints such as pure involution lead to an efficient encoding algorithm. On the other hand, the random constraints enable us to use probabilistic methods for analyzing several code properties such as the average cardinality and the average weight distribution.

preprint2011arXiv

Probabilistic Analysis of the Network Reliability Problem on a Random Graph Ensemble

In the field of computer science, the network reliability problem for evaluating the network failure probability has been extensively investigated. For a given undirected graph $G$, the network failure probability is the probability that edge failures (i.e., edge erasures) make $G$ unconnected. Edge failures are assumed to occur independently with the same probability. The main contributions of the present paper are the upper and lower bounds on the expected network failure probability. We herein assume a simple random graph ensemble that is closely related to the Erdős-Rényi random graph ensemble. These upper and lower bounds exhibit the typical behavior of the network failure probability. The proof is based on the fact that the cut-set space of $G$ is a linear space over $\Bbb F_2$ spanned by the incident matrix of $G$. The present study shows a close relationship between the ensemble analysis of the network failure probability and the ensemble analysis of the error detection probability of LDGM codes with column weight 2.

preprint2007arXiv

Average Stopping Set Weight Distribution of Redundant Random Matrix Ensembles

In this paper, redundant random matrix ensembles (abbreviated as redundant random ensembles) are defined and their stopping set (SS) weight distributions are analyzed. A redundant random ensemble consists of a set of binary matrices with linearly dependent rows. These linearly dependent rows (redundant rows) significantly reduce the number of stopping sets of small size. An upper and lower bound on the average SS weight distribution of the redundant random ensembles are shown. From these bounds, the trade-off between the number of redundant rows (corresponding to decoding complexity of BP on BEC) and the critical exponent of the asymptotic growth rate of SS weight distribution (corresponding to decoding performance) can be derived. It is shown that, in some cases, a dense matrix with linearly dependent rows yields asymptotically (i.e., in the regime of small erasure probability) better performance than regular LDPC matrices with comparable parameters.