Tootfinder

Testing the variety hypothesis
A. Lerario, P. Roos Hoefgeest, M. Scolamiero, A. Tamai
https://arxiv.org/abs/2507.16705 https://arxiv.…

Testing the variety hypothesis
Given a probability measure on the unit disk, we study the problem of deciding whether, for some threshold probability, this measure is supported near a real algebraic variety of given dimension and bounded degree. We call this "testing the variety hypothesis". We prove an upper bound on the so-called "sample complexity" of this problem and show how it can be reduced to a semialgebraic decision problem. This is done by studying in a quantitative way the Hausdorff geometry of the space of real a…

Low-Complexity Ordered Reliability Direct Error Pattern Testing (ORDEPT) Decoding with Likelihood Thresholding
Reza Hadavian, Dmitri Truhachev
https://arxiv.org/abs/2506.20079

Low-Complexity Ordered Reliability Direct Error Pattern Testing (ORDEPT) Decoding with Likelihood Thresholding
We propose a reduced complexity approach to pattern-based soft decoding of block codes. We start from the ORDEPT decoding algorithm which tests a list of partial error patterns organized in the order of their likelihood and attempts to complete the patterns creating candidate codewords. We then propose an early termination criterion. Once a candidate codeword is found, its log-likelihood difference to the received sequence is compared to a preset threshold and the decoding decision is instantly…