Publications

2025

1. Preprint

   

   Universal Decoding over Finite-State Additive Channels via Noise Guessing

   Henrique K. Miyamoto and Sheng Yang

   arXiv, 2025

   Abs arXiv

   We study universal decoding over unknown discrete additive channels determined by a finite-state (unifilar) random process. Aiming at low-complexity decoders, we study variants of noise-guessing decoders that use estimators for the probability of a noise sequence when the actual channel law is unknown. A deterministic version produces noise sequences in a fixed order, and a new randomised version draws them at random, until finding a sequence that, subtracted from the received sequence, results in a valid codeword. We show that both strategies are random-coding universal (i.e. have the same random-coding error exponent as the optimal maximum likelihood decoding), and derive upper bounds for their complexity. Numerical examples in additive Markov channels illustrate the proposed methods’ performance, showing that they consistently outperform a more usual training-based strategy.

2. ITW

   On universal decoding over discrete additive channels by noise guessing

   Henrique K. Miyamoto and Sheng Yang

   In IEEE Information Theory Workshop (ITW), Sydney, Australia, to appear, 2025

   Abs HAL

   We study universal decoding over unknown discrete additive channels. Aiming at low-complexity decoders, we study variants of noise-guessing decoders that use estimators for the probability of a noise sequence when the actual channel law is unknown. A deterministic version produces noise sequences in a fixed order, and a new randomised version draws them at random, until finding one that, subtracted from the received sequence, results in a valid codeword. In all cases, we give sufficient conditions on the family of parametric channels for the decoding strategies to be random-coding universal, and derive upper bounds for their complexity. We give examples of common families of channels in which these conditions are satisfied, and a numerical example illustrates the proposed method’s performance.

2024

1. ISIT

   On Universal Decoding over Memoryless Channels with the Krichevsky-Trofimov Estimator

   Henrique K. Miyamoto and Sheng Yang

   In IEEE International Symposium on Information Theory (ISIT), Athens, Greece, 2024

   Abs DOI

   We study the problem of universal decoding over memoryless channels with a decoder based on the Krichevsky-Trofimov estimator. We show that this decoder is random-coding universal for codebooks of any size, i.e., despite being ignorant of the channel in use, it has asymptotically the same random-coding error exponent as the optimal maximum-likelihood decoder for that channel. Then, we incorporate this decoding rule in schemes to decode practical linear block codes and convolutional codes when the channel is unknown to the receiver. Numerical results show that efficient performance can be achieved even for moderate blocklength or constraint length.

2. Inf. Geom.

   

   On closed-form expressions for the Fisher–Rao distance

   Henrique K. Miyamoto, Fábio C. C. Meneghetti, Julianna Pinele, and 1 more author

   Information Geometry, 2024

   Abs DOI arXiv

   The Fisher–Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is a natural choice of Riemannian metric on such manifolds. It has recently been applied to supervised and unsupervised problems in machine learning, in various contexts. Finding closed-form expressions for the Fisher–Rao distance is generally a non-trivial task, and those are only available for a few families of probability distributions. In this survey, we collect examples of closed-form expressions for the Fisher–Rao distance of both discrete and continuous distributions, aiming to present them in a unified and accessible language. In doing so, we also: illustrate the relation between negative multinomial distributions and the hyperbolic model, include a few new examples, and write a few more in the standard form of elliptical distributions.

2023

1. CNMAC

   Geometria, Estatística e Aplicações a Comunicações e Aprendizado

   Henrique K. Miyamoto

   Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, in Portuguese, 2023

   Abs DOI

   Esta dissertação é composta por três contribuições, que têm em comum a utilização de ferramentas de geometria e/ou estatística em aplicações a comunicações e aprendizado. A primeira trata da construção de códigos esféricos a partir de um procedimento recursivo que se baseia em folheações de esferas dadas pela fibração de Hopf. Na segunda, propomos um método de compressão vetorial com perdas, formado por um quantizador adaptável aos dados, seguido de compressão dos índices de quantização com um algoritmo de árvores de contexto. A terceira consiste em usar uma função perda baseada na distância de Fisher–Rao da variedade de distribuições discretas para o treinamento de redes neurais, particularmente sob ruído de rótulo.

2. Inf. Geom.

   

   The Fisher–Rao loss for learning under label noise

   Henrique K. Miyamoto, Fábio C. C. Meneghetti, and Sueli I. R. Costa

   Information Geometry, 2023

   Abs DOI arXiv

   Choosing a suitable loss function is essential when learning by empirical risk minimisation. In many practical cases, the datasets used for training a classifier may contain incorrect labels, which prompts the interest for using loss functions that are inherently robust to label noise. In this paper, we study the Fisher–Rao loss function, which emerges from the Fisher–Rao distance in the statistical manifold of discrete distributions. We derive an upper bound for the performance degradation in the presence of label noise, and analyse the learning speed of this loss. Comparing with other commonly used losses, we argue that the Fisher–Rao loss provides a natural trade-off between robustness and training dynamics. Numerical experiments with synthetic and MNIST datasets illustrate this performance.

3. GSI

   Revisiting Lattice Tiling Decomposition and Dithered Quantisation

   Fábio C. C. Meneghetti, Henrique K. Miyamoto, Sueli I. R. Costa, and 1 more author

   In Geometric Science of Information, Saint-Malo, France, 2023

   Abs DOI

   A lattice tiling decomposition induces dual operations: quantisation and wrapping, which map the Euclidean space to the lattice and to one of its fundamental domains, respectively. Applying such decomposition to random variables over the Euclidean space produces quantised and wrapped random variables. In studying the characteristic function of those, we show a ‘frequency domain’ characterisation for deterministic quantisation, which is dual to the known ‘frequency domain’ characterisation of uniform wrapping. In a second part, we apply the tiling decomposition to describe dithered quantisation, which consists in adding noise during quantisation to improve its perceived quality. We propose a non-collaborative type of dithering and show that, in this case, a wrapped dither minimises the Kullback-Leibler divergence to the original distribution. Numerical experiments illustrate this result.

2022

1. IEEE-TCOMM

   

   Context-Tree-Based Lossy Compression and Its Application to CSI Representation

   Henrique K. Miyamoto and Sheng Yang

   IEEE Transactions on Communications, 2022

   Abs DOI arXiv

   We propose novel compression algorithms for time-varying channel state information (CSI) in wireless communications. The proposed scheme combines (lossy) vector quantisation and (lossless) compression. First, the new vector quantisation technique is based on a class of parametrised companders applied on each component of the normalised CSI vector. Our algorithm chooses a suitable compander in an intuitively simple way whenever empirical data are available. Then, the sequences of quantisation indices are compressed using a context-tree-based approach. Essentially, we update the estimate of the conditional distribution of the source at each instant and encode the current symbol with the estimated distribution. The algorithms have low complexity, are linear-time in both the spatial dimension and time duration, and can be implemented in an online fashion. We run simulations to demonstrate the effectiveness of the proposed algorithms in such scenarios.

2. MaxEnt

   Information Properties of a Random Variable Decomposition through Lattices

   Fábio C. C. Meneghetti, Henrique K. Miyamoto, and Sueli I. R. Costa

   Physical Sciences Forum, presented at the 41st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt), Paris, France, 2022

   Abs DOI

   A full-rank lattice in the Euclidean space is a discrete set formed by all integer linear combinations of a basis. Given a probability distribution on \(\mathbb{R}^n\), two operations can be induced by considering the quotient of the space by such a lattice: wrapping and quantization. For a lattice \(Λ\), and a fundamental domain \(\mathcal{D}\), which tiles \(\mathbb{R}^n\) through \(Λ\), the wrapped distribution over the quotient is obtained by summing the density over each coset, while the quantized distribution over the lattice is defined by integrating over each fundamental domain translation. These operations define wrapped and quantized random variables over \(\mathcal{D}\) and \(Λ\), respectively, which sum up to the original random variable. We investigate information-theoretic properties of this decomposition, such as entropy, mutual information and the Fisher information matrix, and show that it naturally generalizes to the more abstract context of locally compact topological groups.

3. IZS

   A CSI Compression Scheme Using Context Trees

   Henrique K. Miyamoto and Sheng Yang

   In International Zurich Seminar on Information and Communication (IZS), 2022

   Abs DOI

   We propose novel compression algorithms for timevarying channel state information (CSI) in wireless communications. The proposed schemes combine (lossy) vector quantisation and (lossless) compression. The vector quantisation technique is based on data-adapted parametrised companders applied on each component of the normalised vector. Then, the sequences of quantisation indices are compressed according to estimated distributions computed with a context-tree approach. The algorithms have low complexity, are linear-time in spatial dimension and time duration, and can be implemented in an online fashion. We run numerical experiments to demonstrate the effectiveness of the proposed algorithms in such scenarios.

4. Master’s thesis

   Geometria, estatística e aplicações a comunicações e aprendizado

   Henrique K. Miyamoto

   Universidade Estadual de Campinas, in Portuguese, 2022

   Awarded DOI PDF Errata

   Received the Clóvis Caesar Gonzaga Award for best master’s dissertation in applied and computational mathematics (SBMAC 2023).

2021

1. IEEE-TIT

   

   Constructive Spherical Codes by Hopf Foliations

   Henrique K. Miyamoto, Sueli I. R. Costa, and Henrique N. Sá Earp

   IEEE Transactions on Information Theory, 2021

   Abs DOI arXiv

   We present a new systematic approach to constructing spherical codes in dimensions \(2^k\), based on Hopf foliations. Using the fact that a sphere \(S^{2n-1}\) is foliated by manifolds \(S^{n-1}_{\cosη} \times S^{n-1}_{\sinη}\), \(η∈\left[0,\pi/2\right]\), we distribute points in dimension \(2^k\) via a recursive algorithm from a basic construction in \(\mathbb{R}^4\). Our procedure outperforms some current constructive methods in several small-distance regimes and constitutes a compromise between achieving a large number of codewords for a minimum given distance and effective constructiveness with low encoding computational cost. Bounds for the asymptotic density are derived and compared with other constructions. The encoding process has storage complexity \(O(n)\) and time complexity \(O(n \log n)\). We also propose a sub-optimal decoding procedure, which does not require storing the codebook and has time complexity \(O(n \log n)\).

2019

1. ISIT

   Constructive spherical codes in \(2^k\)dimensions

   Henrique K. Miyamoto, Henrique N. Sá Earp, and Sueli I. R. Costa

   In IEEE International Symposium on Information Theory (ISIT), Paris, France, 2019

   Abs DOI

   We present a new approach to construct spherical codes in \(2^k\) dimensions, based on Hopf foliations. Using the fact that a sphere \(S^{2n-1}\) is foliated by manifolds \(S^{n-1}_{\cosη} \times S^{n-1}_{\sinη}\), \(η∈\left[0,\pi/2\right]\), we distribute points in dimension \(2^k\) via a recursive algorithm from a basic construction in \(\mathbb{R}^4\). Our procedure outperforms some current constructive methods in several small-distance regimes and constitutes a compromise between optimality and computational effort.