arXiv subjects

Hariprasad Manjunath

Publications and source records attributed to Hariprasad Manjunath.

6 recordsLinked to original sources

arXiv2026

Circular Super patterns and Zigzag constructions

In this article, we introduce the notion of circular k-superpatterns, defined as permutations that contain all length-k patterns up to rotation equivalence. We present a construction of a circular superpattern from a linear (k-1)-superpattern and explicitly derive an upper bound on its length. Motivated by the zigzag framework of Engen and Vatter, we adapt and simplify their score function to the circular setting and analyze its parity properties. For odd k, we propose a candidate zigzag construction for circular superpatterns, supported by computational evidence for small values of k.

math.GM↗

arXiv2025

Local Information-Theoretic Security via Euclidean Geometry

This paper introduces a methodology based on Euclidean information theory to investigate local properties of secure communication over discrete memoryless wiretap channels. We formulate a constrained optimization problem that maximizes a legitimate user's information rate while imposing explicit upper bounds on both the information leakage to an eavesdropper and the informational cost of encoding the secret message. By leveraging local geometric approximations, this inherently non-convex problem is transformed into a tractable quadratic programming structure. It is demonstrated that the optimal Lagrange multipliers governing this approximated problem can be found by solving a linear program. The constraints of this linear program are derived from Karush-Kuhn-Tucker conditions and are expressed in terms of the generalized eigenvalues of channel-derived matrices. This framework facilitates the derivation of an analytical formula for an approximate local secrecy capacity. Furthermore, we define and analyze a new class of secret local contraction coefficients. These coefficients, characterized as the largest generalized eigenvalues of a matrix pencil, quantify the maximum achievable ratio of approximate utility to approximate leakage, thus measuring the intrinsic local leakage efficiency of the channel. We establish bounds connecting these local coefficients to their global counterparts defined over true mutual information measures. The efficacy of the proposed framework is demonstrated through detailed analysis and numerical illustrations for both general multi-mode channels and the canonical binary symmetric wiretap channel.

cs.IT↗

arXiv2025

Sparse Regression Codes for Secret Key Agreement: Achieving Strong Secrecy and Near-Optimal Rates for Gaussian Sources

Secret key agreement from correlated physical layer observations is a cornerstone of information-theoretic security. This paper proposes and rigorously analyzes a complete, constructive protocol for secret key agreement from Gaussian sources using Sparse Regression Codes (SPARCs). Our protocol systematically leverages the known optimality of SPARCs for both rate-distortion and Wyner-Ziv (WZ) coding, facilitated by their inherent nested structure. The primary contribution of this work is a comprehensive end-to-end analysis demonstrating that the proposed scheme achieves near-optimal secret key rates with strong secrecy guarantees, as quantified by a vanishing variational distance. We explicitly characterize the gap to the optimal rate, revealing a fundamental trade-off between the key rate and the required public communication overhead, which is governed by a tunable quantization parameter. Furthermore, we uncover a non-trivial constrained optimization for this parameter, showing that practical constraints on the SPARC code parameters induce a peak in the achievable secret key rate. This work establishes SPARCs as a viable and theoretically sound framework for secure key generation, providing a compelling low-complexity alternative to existing schemes and offering new insights into the practical design of such protocols.

cs.IT↗

arXiv2025

Multi-Community Spectral Clustering for Geometric Graphs

In this paper, we consider the soft geometric block model (SGBM) with a fixed number $k \geq 2$ of homogeneous communities in the dense regime, and we introduce a spectral clustering algorithm for community recovery on graphs generated by this model. Given such a graph, the algorithm produces an embedding into $\mathbb{R}^{k-1}$ using the eigenvectors associated with the $k-1$ eigenvalues of the adjacency matrix of the graph that are closest to a value determined by the parameters of the model. It then applies $k$-means clustering to the embedding. We prove weak consistency and show that a simple local refinement step ensures strong consistency. A key ingredient is an application of a non-standard version of Davis-Kahan theorem to control eigenspace perturbations when eigenvalues are not simple. We also analyze the limiting spectrum of the adjacency matrix, using a combination of combinatorial and matrix techniques.

cs.SI↗

arXiv2024

Local Approximation of Secrecy Capacity

This paper uses Euclidean Information Theory (EIT) to analyze the wiretap channel. We investigate a scenario of efficiently transmitting a small amount of information subject to compression rate and secrecy constraints. We transform the information-theoretic problem into a linear algebra problem and obtain the perturbed probability distributions such that secrecy is achievable. Local approximations are being used in order to obtain an estimate of the secrecy capacity by solving a generalized eigenvalue problem.

cs.IT↗

arXiv2022

Spectrum of MATLABs magic squares

This article looks at the eigenvalues of magic squares generated by the MATLAB's magic($n$) function. The magic($n$) function constructs doubly even ($n = 4k$) magic squares, singly even ($n = 4k+2$) magic squares and odd ($n = 2k+1$) magic squares using different algorithms. The doubly even magic squares are constructed by a criss-cross method that involves reflecting the entries of a simple square about the center. The odd magic squares are constructed using the Siamese method. The singly even magic squares are constructed using a lower-order odd magic square (Strachey method). We obtain approximations of eigenvalues of odd and singly even magic squares and prove error bounds on the approximation. For the sake of completeness, we also obtain the eigenpairs of doubly even magic squares generated by MATLAB. The approximation of the spectra involves some interesting connections with the spectrum of g-circulant matrices and the use of Bauer-Fike theorem.

math.GM↗