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Thinh Nguyen

Thinh Nguyen appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Information Theorymath.ITeess.SPInformation RetrievalMachine Learningmath-phmath.MPmath.PRquant-phSystems and Control

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Published work

11 published item(s)

preprint2026arXiv

Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling

This paper studies cross-domain lossy compression through the lens of minimum entropy coupling (MEC) with rate and classification constraints. In this setting, an encoder observes samples from a degraded source domain, while the decoder is required to generate outputs following a prescribed target distribution and to preserve information relevant to a downstream classification task. Motivated by logarithmic-loss distortion, we adopt an information-based objective that maximizes the coupling strength between the source and reconstruction, rather than minimizing a sample-wise distortion. Under common randomness, we formulate a rate-constrained MEC problem (MEC-B) and show that the intermediate representation can be removed without loss of optimality, yielding an equivalent deterministic coupling formulation. For Bernoulli sources, closed-form expressions are derived with and without classification constraints. In addition, we implement a neural restoration framework using quantization, entropy modeling, distribution matching, and classification regularization. Experiments on MNIST super-resolution and SVHN denoising show that increasing the available rate improves classification accuracy and yields more informative reconstructions.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Communication-Channel Optimized Partition

Given an original discrete source X with the distribution p_X that is corrupted by noise to produce the noisy data Y with the given joint distribution p(X, Y). A quantizer/classifier Q : Y -> Z is then used to classify/quantize the data Y to the discrete partitioned output Z with probability distribution p_Z. Next, Z is transmitted over a deterministic channel with a given channel matrix A that produces the final discrete output T. One wants to design the optimal quantizer/classifier Q^* such that the cost function F(X; T) between the input X and the final output T is minimized while the probability of the partitioned output Z satisfies a concave constraint G(p_Z) < C. Our results generalized some famous previous results. First, an iteration linear time complexity algorithm is proposed to find the local optimal quantizer. Second, we show that the optimal partition should produce a hard partition that is equivalent to the cuts by hyper-planes in the probability space of the posterior probability p(X|Y). This result finally provides a polynomial-time algorithm to find the globally optimal quantizer.

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preprint2020arXiv

Entropy-Constrained Maximizing Mutual Information Quantization

In this paper, we investigate the quantization of the output of a binary input discrete memoryless channel that maximizing the mutual information between the input and the quantized output under an entropy-constrained of the quantized output. A polynomial time algorithm is introduced that can find the truly global optimal quantizer. These results hold for binary input channels with an arbitrary number of quantized output. Finally, we extend these results to binary input continuous output channels and show a sufficient condition such that a single threshold quantizer is an optimal quantizer. Both theoretical results and numerical results are provided to justify our techniques.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

On Bounds and Closed Form Expressions for Capacities of Discrete Memoryless Channels with Invertible Positive Matrices

While capacities of discrete memoryless channels are well studied, it is still not possible to obtain a closed-form expression for the capacity of an arbitrary discrete memoryless channel. This paper describes an elementary technique based on Karush Kuhn Tucker (KKT) conditions to obtain (1) a good upper bound of a discrete memoryless channel having an invertible positive channel matrix and (2) a closed-form expression for the capacity if the channel matrix satisfies certain conditions related to its singular value and its Gershgorin disk.

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preprint2020arXiv

On the Uniqueness of Binary Quantizers for Maximizing Mutual Information

We consider a channel with a binary input X being corrupted by a continuous-valued noise that results in a continuous-valued output Y. An optimal binary quantizer is used to quantize the continuous-valued output Y to the final binary output Z to maximize the mutual information I(X; Z). We show that when the ratio of the channel conditional density r(y) = P(Y=y|X=0)/ P(Y =y|X=1) is a strictly increasing/decreasing function of y, then a quantizer having a single threshold can maximize mutual information. Furthermore, we show that an optimal quantizer (possibly with multiple thresholds) is the one with the thresholding vector whose elements are all the solutions of r(y) = r* for some constant r* > 0. Interestingly, the optimal constant r* is unique. This uniqueness property allows for fast algorithmic implementation such as a bisection algorithm to find the optimal quantizer. Our results also confirm some previous results using alternative elementary proofs. We show some numerical examples of applying our results to channels with additive Gaussian noises.

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preprint2020arXiv

Optimal quantizer structure for binary discrete input continuous output channels under an arbitrary quantized-output constraint

Given a channel having binary input X = (x_1, x_2) having the probability distribution p_X = (p_{x_1}, p_{x_2}) that is corrupted by a continuous noise to produce a continuous output y \in Y = R. For a given conditional distribution p(y|x_1) = ϕ_1(y) and p(y|x_2) = ϕ_2(y), one wants to quantize the continuous output y back to the final discrete output Z = (z_1, z_2, ..., z_N) with N \leq 2 such that the mutual information between input and quantized-output I(X; Z) is maximized while the probability of the quantized-output p_Z = (p_{z_1}, p_{z_2}, ..., p_{z_N}) has to satisfy a certain constraint. Consider a new variable r_y=p_{x_1}ϕ_1(y)/ (p_{x_1}ϕ_1(y)+p_{x_2}ϕ_2(y)), we show that the optimal quantizer has a structure of convex cells in the new variable r_y. Based on the convex cells property of the optimal quantizers, a fast algorithm is proposed to find the global optimal quantizer in a polynomial time complexity.

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preprint2020arXiv

Single-bit Quantization Capacity of Binary-input Continuous-output Channels

We consider a channel with discrete binary input X that is corrupted by a given continuous noise to produce a continuous-valued output Y. A quantizer is then used to quantize the continuous-valued output Y to the final binary output Z. The goal is to design an optimal quantizer Q* and also find the optimal input distribution p*(X) that maximizes the mutual information I(X; Z) between the binary input and the binary quantized output. A linear time complexity searching procedure is proposed. Based on the properties of the optimal quantizer and the optimal input distribution, we reduced the searching range that results in a faster implementation algorithm. Both theoretical and numerical results are provided to illustrate our method.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Minimizing Impurity Partition Under Constraints

Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there exists a wealth of literature on approximate algorithms and theoretical analyses of the partitioning problem under different settings. In this paper, we formulate and solve a variant of the partition problem called the minimum impurity partition under constraint (MIPUC). MIPUC finds an optimal partition that minimizes a given loss function under a given concave constraint. MIPUC generalizes the recently proposed deterministic information bottleneck problem which finds an optimal partition that maximizes the mutual information between the input and partition output while minimizing the partition output entropy. Our proposed algorithm is developed based on a novel optimality condition, which allows us to find a locally optimal solution efficiently. Moreover, we show that the optimal partition produces a hard partition that is equivalent to the cuts by hyperplanes in the probability space of the posterior probability that finally yields a polynomial time complexity algorithm to find the globally optimal partition. Both theoretical and numerical results are provided to validate the proposed algorithm.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Flatness-based nonlinear control strategies for trajectory tracking of quadcopter systems

This paper proposes several nonlinear control strategies for trajectory tracking of a quadcopter system based on the property of differential flatness. Its originality is twofold. Firstly, it provides a flat output for the quadcopter dynamics capable of creating full flat parametrization of the states and inputs. Moreover, B-splines characterizations of the flat output and their properties allow for optimal trajectory generation subject to way-point constraints. Secondly, several control strategies based on computed torque control and feedback linearization are presented and compared. The advantages of flatness within each control strategy are analyzed and detailed through extensive simulation results.

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preprint2012arXiv

Stable Adiabatic Times for Markov Chains

In this paper we continue our work on adiabatic time of time-inhomogeneous Markov chains first introduced in Kovchegov (2010) and Bradford and Kovchegov (2011). Our study is an analog to the well-known Quantum Adiabatic (QA) theorem which characterizes the quantum adiabatic time for the evolution of a quantum system as a result of applying of a series of Hamilton operators, each is a linear combination of two given initial and final Hamilton operators, i.e. $\mathbf{H}(s) = (1-s)\mathbf{H_0} + s\mathbf{H_1}$. Informally, the quantum adiabatic time of a quantum system specifies the speed at which the Hamiltonian operators changes so that the ground state of the system at any time $s$ will always remain $ε$-close to that induced by the Hamilton operator $\mathbf{H}(s)$ at time $s$. Analogously, we derive a sufficient condition for the stable adiabatic time of a time-inhomogeneous Markov evolution specified by applying a series of transition probability matrices, each is a linear combination of two given irreducible and aperiodic transition probability matrices, i.e., $\mathbf{P_{t}} = (1-t)\mathbf{P_{0}} + t\mathbf{P_{1}}$. In particular we show that the stable adiabatic time $t_{sad}(\mathbf{P_{0}}, \mathbf{P_{1}}, ε) = O (t_{mix}^{4}(ε\slash 2) \slash ε^{3}), $ where $t_{mix}$ denotes the maximum mixing time over all $\mathbf{P_{t}}$ for $0 \leq t \leq 1$.

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preprint2011arXiv

Framework for discrete-time quantum walks and a symmetric walk on a binary tree

We formulate a framework for discrete-time quantum walks, motivated by classical random walks with memory. We present a specific representation of the classical walk with memory 2 on which this is based. The framework has no need for coin spaces, it imposes no constraints on the evolution operator other than unitarity, and is unifying of other approaches. As an example we construct a symmetric discrete-time quantum walk on the semi-infinite binary tree. The generating function of the amplitude at the root is computed in closed-form, as a function of time and the initial level n in the tree, and we find the asymptotic and a full numerical solution for the amplitude. It exhibits a sharp interference peak and a power law tail, as opposed to the exponentially decaying tail of a broadly peaked distribution of the classical symmetric random walk on a binary tree. The probability peak is orders of magnitude larger than it is for the classical walk (already at small n). The quantum walk shows a polynomial algorithmic speedup in n over the classical walk, which we conjecture to be of the order 2/3, based on strong trends in data.

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