Year: 2019
Type: preprint
Abstract: Construction of error-correcting codes achieving a designated minimum distance parameter is a central problem in coding theory. In this work, we study a very simple construction of binary linear codes that correct a given number of errors $K$. Moreover, we design a simple, nearly optimal syndrome decoder for the code as well. The running time of the decoder is only logarithmic in the block length of the code, and nearly linear in the number of errors $K$. This decoder can be applied to exact for-all sparse recovery over any field, improving upon previous results with the same number of measurements. Furthermore, computation of the syndrome from a received word can be done in nearly linear time in the block length. We also demonstrate an application of these techniques in non-adaptive group testing, and construct simple explicit measurement schemes with $O(K^2 \log^2 N)$ tests and $O(K^3 \log^2 N)$ recovery time for identifying up to $K$ defectives in a population of size $N$.
Source: arXiv (Cornell University)
Authors: Cheraghchi, Mahdi, Ribeiro, João
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: CIF: AF: Small: Data Processing Against Synchronization Errors, CIF: Small: New Coding Techniques for Synchronization Errors, SaTC: CORE: Small: Transforming Non-Malleable Cryptography, Collaborative Research: CIF: Medium: Group testing for Real-Time Polymerase Chain Reactions: From Primer Selection to Amplification Curve Analysis, Collaborative Research: CIF: Medium: Group testing for Real-Time Polymerase Chain Reactions: From Primer Selection to Amplification Curve Analysis
OpenAlex ID: W4288639809