arXiv subjects

Nazanin Mirhosseini

Publications and source records attributed to Nazanin Mirhosseini.

3 recordsLinked to original sources

arXiv2026

On Geometric Asymmetry and Information in Sequential Dimension Reduction

Standard random projection techniques operate as a black box, mapping high-dimensional structures directly to a lower-dimensional space where the target dimension must be specified a \textit{priori}. To address scenarios where the ultimate dimension is unknown, this paper investigates the retention of information through a sequential dimension reduction process. We examine a fixed, bounded convex body as it undergoes successive random orthogonal projections, systematically reducing the ambient dimension by one at each step. By demonstrating that this sequence of bodies forms a Markov chain, we quantify the information preserved through these reductions using the conditional mutual information between successive projections given the original convex body. We derive an upper bound on this conditional mutual information, parameterized by the Haar measure of the projection spaces that yield the same observed body. Leveraging the established Markov property, we extend these results to an arbitrary number of iterations, proving that the initial two-step bound characterizes information retention across the entire sequence of projections. Furthermore, analyzing the initial body's symmetry group projections reveals that geometric asymmetry enhances information retention.

eess.SP↗

arXiv2026

Hemispherical Concentration Subset Recovery in Many-Access Gaussian Multiple-Access Channels

We consider subset recovery in the many-access Gaussian multiple-access channel with a shared spherical codebook, where codewords are drawn independently and uniformly from the hypersphere of radius $ \sqrt{nP} $, the number of active users scales linearly with the blocklength $n$ as $ K_a(n)=βn $ for a constant $ β> 0 $, and the codebook size is $ M_n=n^d $ with $ d>2 $. We identify a geometric property showing that, for $ 0<β<2 $, any transmitted $ K_a(n) $-subset lies in a single hemisphere with high probability for sufficiently large $n$. We further show that reliable decoding is possible only for $ β< 1/4 $. The overlap between the reliable decoding range of $ β$ and the hemispherical concentration range motivates our approach of two-stage decoding procedure. In the pre-filtering stage, the decoder restricts attention to a sequence of spherical caps $ \{ \hat{\mathcal{H}}_n \} $ that converges in Hausdorff distance to the hemisphere $\hat{\mathcal{H}}$, whose axis is the normalized observation $ \hat{\mathbf{u}}=\mathbf{Y}/\|\mathbf{Y}\| $. In the second stage, maximum-likelihood decoding is performed over the reduced candidate set. We show that the per-user error probability of the pre-filtering stage vanishes as $ n\to\infty $. Moreover, the per-user error probability of the maximum-likelihood stage over the reduced search space decays exponentially with asymptotic exponent $ P/4 $.

cs.IT↗

arXiv2025

Unified Error Analysis for Synchronous and Asynchronous Two-User Random Access

We consider a two-user random access system in which each user independently selects a coding scheme from a finite set for every message, without sharing these choices with the other user or with the receiver. The receiver aims to decode only user 1 message but may also decode user 2 message when beneficial. In the synchronous setting, the receiver employs two parallel sub-decoders: one dedicated to decoding user 1 message and another that jointly decodes both users messages. Their outputs are synthesized to produce the final decoding or collision decision. For the asynchronous setting, we examine a time interval containing $L$ consecutive codewords from each user. The receiver deploys $2^{2L}$ parallel sub-decoders, each responsible for decoding a subset of the message-code index pairs. In both synchronous and asynchronous cases, every sub-decoder partitions the coding space into three disjoint regions: operation, margin, and collision, and outputs either decoded messages or a collision report according to the region in which the estimated code index vector lies. Error events are defined for each sub-decoder and for the overall receiver whenever the expected output is not produced. We derive achievable upper bounds on the generalized error performance, defined as a weighted sum of incorrect-decoding, collision, and miss-detection probabilities, for both synchronous and asynchronous scenarios.

cs.IT↗