arXiv subjects

Bella Bose

Publications and source records attributed to Bella Bose.

10 recordsLinked to original sources

arXiv2026

Chi-Squared Geometry for Robust Finite-Blocklength Information and Dispersion Analysis

We develop a column-wise chi-squared geometry for discrete memoryless channels (DMCs) yielding tight, logarithm-free bounds on mutual information, channel dispersion, and finite-blocklength coding rates without evaluating logarithms of the channel matrix. The key parameter is~$\eta$---the worst-case relative deviation of a transition probability from its output marginal, which is small precisely when the channel is close to the fully noisy channel $t_{ij}=s_j$. We prove three main results: (1) a third-order ratio expansion showing $I(X;Y)/\chi^2(X;Y)\to 1/2$ as $\eta\to 0$ with an $O(\eta)$ skewness correction; (2) a two-sided dispersion equivalence bounding $V(X;Y)$ above and below by $\chi^2(X;Y)$ with explicit constants $c_{\pm}(\eta)\to 1$; and (3) a certified robust design rate $R_{\mathrm{cert}}(n,\varepsilon)$ with total certification gap $O(\eta)+O(\eta/\sqrt{n})+O(\log n/n)$. The certified bounds on $I$ and $V$ require only addition, multiplication, division, and square roots; the final rate also uses $Q^{-1}(\varepsilon)$.

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arXiv2026

Combinatorial Capacity Bounds for the $q$-ary Deletion Channel

We study the $q$-ary deletion channel via the pattern-count scalar $N_n(x,y)$, the number of deletion subsets mapping $x\in\Sigma_q^n$ to $y\in\Sigma_q^k$, which factorizes the transition probability. Two sum identities on $N_n$ certify stochastic normalization and, under uniform input, yield an exact closed-form output entropy. These give the finite-block capacity sandwich $ (1-d)\log_2 q-h_2(d)\;\le\; C_{q,n}\;\le\;(1-d)\log_2 q. $ The exact uniform-input rate is $ \frac{1}{n}I_U(X;Y) =(1-d)\log_2 q+\frac{1}{n}H_{\mathrm{Bin}}(n,1-d)-h_2(d)+\frac{\Delta_n(d)}{n}, $ from which the simpler certified bound $ C_{q,n}\ge (1-d)\log_2 q-h_2(d)+\frac{\Delta_n(d)}{n} $ follows. The small-$d$ bound $C_q(d)\ge\log_2 q+d\log_2 d+O(d)$ follows for all $q\ge 2$. Numerical experiments at $n=3,5,10$ and $q=2,3$ confirm all bounds.

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arXiv2026

Parameter Estimation of Mutual Information Maximized Channels

We study the problem of estimating a parametric discrete memoryless channel $ p(y \mid x; \boldsymbol{\theta}) $ when the transmitter selects its input distribution $ \pi $ to maximize mutual information under the true parameter $ \boldsymbol{\theta}^* $. Using only i.i.d.\ observations of the channel output, we aim to jointly estimate the capacity-achieving input distribution $ \boldsymbol{\pi}^* $ and the true channel parameter $ \boldsymbol{\theta}^* $. In general, recovery of $ \boldsymbol{\pi}^* $ and $ \boldsymbol{\theta}^* $ 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 $ \boldsymbol{\theta}^* $ and $ \boldsymbol{\pi}^* $, whereas a naive maximum-likelihood approach that ignores the mutual-information maximization constraint fails to do so.

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arXiv2026

RankGuardPolar Private Public Finite Length Polar Codes with Rank-Certified Leakage

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.

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arXiv2026

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.

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arXiv2026

Perception-based Image Denoising via Generative Compression

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.

cs.CV↗

arXiv2026

Rate-Distortion-Classification Representation Theory for Bernoulli Sources

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.

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arXiv2025

A Theory of Universal Rate-Distortion-Classification Representations for Lossy Compression

In lossy compression, Blau and Michaeli [5] introduced the information rate-distortion-perception (RDP) function, extending traditional rate-distortion theory by incorporating perceptual quality. More recently, this framework was expanded by defining the rate-distortion-perception-classification (RDPC) function, integrating multi-task learning that jointly optimizes generative tasks such as perceptual quality and classification accuracy alongside reconstruction tasks [28]. To that end, motivated by the concept of a universal RDP encoder introduced in [34], we investigate universal representations that enable diverse distortion-classification tradeoffs through a single fixed encoder combined with multiple decoders. Specifically, theoretical analysis and numerical experiment demonstrate that for the Gaussian source under mean squared error (MSE) distortion, the entire distortion-classification tradeoff region can be achieved using one universal encoder. In addition, this paper characterizes achievable distortion-classification regions for fixed universal representations in general source distributions, identifying conditions that ensure minimal distortion penalty when reusing encoders across varying tradeoff points. Experimental results using MNIST and SVHN datasets validate our theoretical insights, showing that universal encoders can obtain distortion performance comparable to task-specific encoders, thus supporting the practicality and effectiveness of our proposed universal representations.

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arXiv2025

Universal Rate-Distortion-Classification Representations for Lossy Compression

In lossy compression, Wang et al. [1] recently introduced the rate-distortion-perception-classification function, which supports multi-task learning by jointly optimizing perceptual quality, classification accuracy, and reconstruction fidelity. Building on the concept of a universal encoder introduced in [2], we investigate the universal representations that enable a broad range of distortion-classification tradeoffs through a single shared encoder coupled with multiple task-specific decoders. We establish, through both theoretical analysis and numerical experiments, that for Gaussian source under mean squared error (MSE) distortion, the entire distortion-classification tradeoff region can be achieved using a single universal encoder. For general sources, we characterize the achievable region and identify conditions under which encoder reuse results in negligible distortion penalty. The experimental result on the MNIST dataset further supports our theoretical findings. We show that universal encoders can obtain distortion performance comparable to task-specific encoders. These results demonstrate the practicality and effectiveness of the proposed universal framework in multi-task compression scenarios.

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arXiv2023

Efficient Systematic Deletions/Insertions of $0$'s Error Control Codes and the $L_{1}$ Metric (Extended version)

This paper gives some theory and efficient design of binary block systematic codes capable of controlling the deletions of the symbol ``$0$'' (referred to as $0$-deletions) and/or the insertions of the symbol ``$0$'' (referred to as $0$-insertions). The problem of controlling $0$-deletions and/or $0$-insertions (referred to as $0$-errors) is known to be equivalent to the efficient design of $L_{1}$ metric asymmetric error control codes over the natural alphabet, $\mathbb{N}$. So, $t$ $0$-insertion correcting codes can actually correct $t$ $0$-errors, detect $(t+1)$ $0$-errors and, simultaneously, detect all occurrences of only $0$-deletions or only $0$-insertions in every received word (briefly, they are $t$-Symmetric $0$-Error Correcting/$(t+1)$-Symmetric $0$-Error Detecting/All Unidirectional $0$-Error Detecting ($t$-Sy$0$EC/$(t+1)$-Sy$0$ED/AU$0$ED) codes). From the relations with the $L_{1}$ distance, optimal systematic code designs are given. In general, for all $t,k\in\mathbb{N}$, a recursive method is presented to encode $k$ information bits into efficient systematic $t$-Sy$0$EC/$(t+1)$-Sy$0$ED/AU$0$ED codes of length $$ n\leq k+t\log_{2}k+o(t\log n) $$ as $n\in\mathbb{N}$ increases. Decoding can be efficiently performed by algebraic means using the Extended Euclidean Algorithm (EEA).

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