arXiv subjects

Hassan Tavakoli

Publications and source records attributed to Hassan Tavakoli.

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~$η$---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 $I(X;Y)/χ^2(X;Y)\to 1/2$ as $η\to 0$ with an $O(η)$ skewness correction; (2) a two-sided dispersion equivalence bounding $V(X;Y)$ above and below by $χ^2(X;Y)$ with explicit constants $c_{\pm}(η)\to 1$; and (3) a certified robust design rate $R_{\mathrm{cert}}(n,\varepsilon)$ with total certification gap $O(η)+O(η/\sqrt{n})+O(\log n/n)$. 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 $x\inΣ_q^n$ to $y\inΣ_q^k$, 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{Δ_n(d)}{n}, $ from which the simpler certified bound $ C_{q,n}\ge (1-d)\log_2 q-h_2(d)+\frac{Δ_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

New Capacity Upper Bounds For Binary Deletion Channel

This paper considers a binary channel with deletions. We derive two closed-form upper bounds on the capacity of the binary deletion channel (BDC). The first bound is obtained by computing the capacity of an auxiliary channel, the two-bit Fixed-length-Input BDC (FI-BDC), and showing that this auxiliary capacity upper-bounds the capacity of the BDC. The second bound is obtained by approximating the mutual information between sent and received bits directly, yielding a closed-form expression parameterized by a first-order Markov correlation parameter $γ$. Both bounds use a first-order Markov process for the channel input. We verify Theorem~1's optimization from first principles, directly from the two-bit auxiliary channel's transition matrix rather than from the mutual-information expression alone: the underlying objective is strictly concave with a unique interior maximizer, and the resulting closed-form bound is confirmed correct. The second proposed upper bound is evaluated against the Fertonani--Duman and Dalai bounds in Fig.~4.

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arXiv2026

Guesswork Under Linear Constraints: Exact Exponent for Coset Decoding

We establish the exact exponential growth rate of the $ρ$-th moment of the constrained guesswork $G_{\mathrm{coset}}$ -- the rank of the true noise vector within its syndrome coset of a random binary linear code under i.i.d.\ Bernoulli$(p)$ noise: $ \lim_{n\to\infty} \frac{1}{n}\log_2\Eb\!\left[G_{\mathrm{coset}}^ρ\right] = ρ\,h_{\frac{1}{1+ρ}}(p)\;+\;ρ(R-1), \, ρ>0, $ where $h_α(p)$ is the binary Rényi entropy and $R=k/n$ is the code rate. The exponent shifts down by exactly $ρ(1-R)$ relative to the unconstrained Arıkan--Merhav exponent, with each of the $n(1-R)$ parity checks contributing equally. Finite-length simulations confirm convergence from below. We further establish: (i)~a transfer theorem expressing the partition-function exponent in terms of an arbitrary weight-enumerator growth rate $g(δ)$; (ii)~the exact exponent for $L_n$-list (``$k$-th'') constrained guesswork; and (iii)~a sharp second-order refinement of order $ρ\log_2 n$. Beyond the binary i.i.d.\ setting, we prove a universality theorem: for any code ensemble $\mathcal{E}$ whose weight enumerator concentrates at rate $g_{\mathcal{E}}(δ)$, the guesswork exponent equals $(1+ρ)ψ_{1/(1+ρ)}(g_{\mathcal{E}})-ρ\,ψ_1(g_{\mathcal{E}})$, where $ψ_α(g)=\sup_δ[g(δ)+α\ell(δ)]$. As concrete applications, we instantiate this theorem for the $q$-ary extension, $Λ_q(ρ)=ρ\,h^{(q)}_{1/(1+ρ)}(P)+ρ(R-1)\log_2 q$, and for Gallager's regular LDPC ensemble, obtaining a closed-form guesswork exponent via an exact finite-length identity for the ensemble-average weight enumerator.

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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; \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.

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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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arXiv2014

A Fast Convergence Density Evolution Algorithm for Optimal Rate LDPC Codes in BEC

We derive a new fast convergent Density Evolution algorithm for finding optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure channel (BEC). The fast convergence property comes from the modified Density Evolution (DE), a numerical method for analyzing the behavior of iterative decoding convergence of a LDPC code. We have used the method of [16] for designing of a LDPC code with optimal rate. This has been done for a given parity check node degree distribution, erasure probability and specified DE constraint. The fast behavior of DE and found optimal rate with this method compare with the previous DE constraint.

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arXiv2014

Reducing the Complexity of the Linear Programming Decoding

In this paper we show how the complexity of Linear Programming (LP) decoder can decrease. We use the degree 3 check equation to model all variation check degrees. The complexity of LP decoding is directed relative to the number of constraint. Number of constraint for original LP decoder is O(n*(2^n)). Our method decrease the number of the constraint to O(n).

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arXiv2014

Source and Channel Optimal Rate LDPC Code Design for one Sender in BE-MAC with Source Correlation

In this paper, we present an extension of the semidefinite programming formulation of the optimal rate code design in single link Binary Erasure Channel (BEC) proposed by the authors to the Binary Erasure Multiple Access Channel (BE-MAC) with two sources correlation. This new way can be easily extended to the multiple access senders. Simulation results show the efficiency and effectiveness of the new approach in practice.

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