Bella Bose

Nam Nguyen, Thinh Nguyen, Bella Bose

We study task-oriented lossy compression through the lens of rate-distortion-classification (RDC) representations. The source is Bernoulli, the distortion measure is Hamming, and the binary classification variable is coupled to the source via a binary symmetric model. Building on the one-shot common-randomness formulation, we first derive closed-form characterizations of the one-shot RDC and the dual distortion-rate-classification (DRC) tradeoffs. We then use a representation-based viewpoint and characterize the achievable distortion-classification (DC) region induced by a fixed representation by deriving its lower boundary via a linear program. Finally, we study universal encoders that must support a family of DC operating points and derive computable lower and upper bounds on the minimum asymptotic rate required for universality, thereby yielding bounds on the corresponding rate penalty. Numerical examples are provided to illustrate the achievable regions and the resulting universal RDC/DRC curves.

Hassan Tavakoli, Thinh Nguyen, Bella Bose

We study the problem of estimating a parametric discrete memoryless channel \( p(y \mid x; \boldsymbolθ) \) when the transmitter selects its input distribution \( π\) to maximize mutual information under the true parameter \( \boldsymbolθ^* \). Using only i.i.d.\ observations of the channel output, we aim to jointly estimate the capacity-achieving input distribution \( \boldsymbolπ^* \) and the true channel parameter \( \boldsymbolθ^* \). In general, recovery of \( \boldsymbolπ^* \) and \( \boldsymbolθ^* \) can be challenging. To that end, we propose two efficient algorithms based on the Blahut--Arimoto (BA) optimality conditions: (i) a bilevel fixed-point method and (ii) an augmented Lagrangian method. Empirical results demonstrate that both proposed algorithms successfully recover the true \( \boldsymbolθ^* \) and \( \boldsymbolπ^* \), whereas a naive maximum-likelihood approach that ignores the mutual-information maximization constraint fails to do so.

Hassan Tavakoli, Thinh Nguyen, Bella Bose

We introduce \textbf{RankGuard-Polar}, a framework for safely publishing a subset of polar codeword coordinates over shared public resources. We assume a strong eavesdropper who has access to the channel input, i.e., the transmitted codeword coordinates published on a public resource access model. Working over \(\mathbb F_2\) and focusing on time-shared public/private BEC uses, we show that leakage from a published index set \(\mathbf{P}\) admits an exact algebraic characterization comes from an information-theoretic viewpoint, and we construct an explicit linear extractor ($R$) that identifies the leaked linear combinations. Building on this identity, we (i) give efficient procedures to compute and certify leakage for any \(\mathbf{P}\), (ii) propose a practical fast algorithm with provable efficiency.

Nam Nguyen, Hassan Tavakoli, An Vuong et al.

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.

Nam Nguyen, Thinh Nguyen, Bella Bose

Image denoising aims to remove noise while preserving structural details and perceptual realism, yet distortion-driven methods often produce over-smoothed reconstructions, especially under strong noise and distribution shift. This paper proposes a generative compression framework for perception-based denoising, where restoration is achieved by reconstructing from entropy-coded latent representations that enforce low-complexity structure, while generative decoders recover realistic textures via perceptual measures such as learned perceptual image patch similarity (LPIPS) loss and Wasserstein distance. Two complementary instantiations are introduced: (i) a conditional Wasserstein GAN (WGAN)-based compression denoiser that explicitly controls the rate-distortion-perception (RDP) trade-off, and (ii) a conditional diffusion-based reconstruction strategy that performs iterative denoising guided by compressed latents. We further establish non-asymptotic guarantees for the compression-based maximum-likelihood denoiser under additive Gaussian noise, including bounds on reconstruction error and decoding error probability. Experiments on synthetic and real-noise benchmarks demonstrate consistent perceptual improvements while maintaining competitive distortion performance.