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Function-correcting codes are a coding framework designed to minimize redundancy while ensuring that specific functions or computations of encoded data can be reliably recovered, even in the presence of errors. The choice of metric is…

Information Theory · Computer Science 2026-02-18 Gyanendra K. Verma , Abhay Kumar Singh

We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over…

Information Theory · Computer Science 2011-05-10 Rathinakumar Appuswamy , Massimo Franceschetti , Nikhil Karamchandani , Kenneth Zeger

In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…

Computational Complexity · Computer Science 2007-05-23 Asa Ben-Hur , Joshua Feinberg , Shmuel Fishman , Hava T. Siegelmann

Function-correcting codes (FCCs) are designed to provide error protection for the value of a function computed on the data. Existing work typically focuses solely on protecting the function value and not the underlying data. In this work,…

Information Theory · Computer Science 2026-05-20 Charul Rajput , B. Sundar Rajan , Ragnar Freij-Hollanti , Camilla Hollanti

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same…

Data Analysis, Statistics and Probability · Physics 2023-06-16 Dmitri Martila , Stefan Groote

A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…

Information Theory · Computer Science 2012-05-22 Dung Viet Nguyen , Bane Vasic , Michael W. Marcellin

Estimating the ratio of two probability densities from a finite number of observations is a central machine learning problem. A common approach is to construct estimators using binary classifiers that distinguish observations from the two…

Machine Learning · Computer Science 2025-01-28 Werner Zellinger

In this paper, we introduce a class of functions that assume only a limited number $\lambda$ of values within a given Hamming $\rho$-ball and call them locally $(\rho, \lambda)$-bounded functions. We develop function-correcting codes (FCCs)…

Information Theory · Computer Science 2025-11-14 Charul Rajput , B. Sundar Rajan , Ragnar Freij-Hollanti , Camilla Hollanti

We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…

Combinatorics · Mathematics 2024-06-25 Aida Abiad , Alexander L. Gavrilyuk , Antonina P. Khramova , Ilia Ponomarenko

In this paper, we present a general review of hash functions in a cryptographic sense. We give special emphasis on some particular topics such as cipher block chaining message authentication code (CBC MAC) and its variants. This paper also…

Cryptography and Security · Computer Science 2007-05-23 Turker Ozsari

The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, $k$-error linear complexity, the minimum error and the $k$-error linear complexity…

Cryptography and Security · Computer Science 2011-09-22 Jianqin Zhou , Wei Xiong

We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as…

Information Theory · Computer Science 2007-07-13 Elitza N. Maneva , Amin Shokrollahi

We present techniques for speeding up the test-time evaluation of large convolutional networks, designed for object recognition tasks. These models deliver impressive accuracy but each image evaluation requires millions of floating point…

Computer Vision and Pattern Recognition · Computer Science 2024-03-15 Remi Denton , Wojciech Zaremba , Joan Bruna , Yann LeCun , Rob Fergus

Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and…

Information Theory · Computer Science 2007-07-13 Igal Sason , Shlomo Shamai

Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…

Machine Learning · Computer Science 2023-02-24 Subha Maity , Debarghya Mukherjee , Moulinath Banerjee , Yuekai Sun

Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems motivates investigating the feasibility of…

A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…

Numerical Analysis · Mathematics 2023-02-17 Matthias Grajewski , Andreas Kleefeld

A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…

Machine Learning · Computer Science 2017-12-25 Mohammad Reza Bonyadi , Viktor Vegh , David C. Reutens

Locally Decodable Codes (LDCs) are error-correcting codes for which individual message symbols can be quickly recovered despite errors in the codeword. LDCs for Hamming errors have been studied extensively in the past few decades, where a…

Information Theory · Computer Science 2025-12-30 Jeremiah Blocki , Kuan Cheng , Elena Grigorescu , Xin Li , Yu Zheng , Minshen Zhu

Countless applications cast their computational core in terms of dense linear algebra operations. These operations can usually be implemented by combining the routines offered by standard linear algebra libraries such as BLAS and LAPACK,…

Performance · Computer Science 2014-10-01 Elmar Peise , Paolo Bientinesi