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The idea of rare event sampling is applied to the estimation of the performance of error-correcting codes. The essence of the idea is importance sampling of the pattern of noises in the channel by Multicanonical Monte Carlo, which enables…
Randomness is a crucial resource for a broad range of important applications, such as Monte Carlo simulation and computation, generative artificial intelligence and cryptography. But what is randomness? A widely accepted definition has…
Large language models make remarkable progress in reasoning capabilities. Existing works focus mainly on deductive reasoning tasks (e.g., code and math), while another type of reasoning mode that better aligns with human learning, inductive…
Research at the intersection of machine learning, programming languages, and software engineering has recently taken important steps in proposing learnable probabilistic models of source code that exploit code's abundance of patterns. In…
Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing…
A new kind of Convolutional Codes generalizing Goppa Codes is proposed. This provides a systematic method for constructing convolutional codes with prefixed properties. In particular, examples of Maximum-Distance Separable (MDS)…
We suggest a method for generation of random binary sequences with prescribed correlation properties. It is based on a kind of modification of the widely used convolution method of constructing continuous random processes. Apart from the…
A general method for constructing convolutional codes from units in Laurent series over matrix rings is presented. Using group ring as matrix rings, this forms a basis for in-depth exploration of convolutional codes from group ring…
Random numbers play a crucial role in science and industry. Many numerical methods require the use of random numbers, in particular the Monte Carlo method. Therefore it is of paramount importance to have efficient random number generators.…
A modification of Koetter-Kschischang codes for random networks is presented (these codes were also studied by Wang et al. in the context of authentication problems). The new codes have higher information rate, while maintaining the same…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
In Search Based Software Engineering, Genetic Programming has been used for bug fixing, performance improvement and parallelisation of programs through the modification of source code. Where an evolutionary computation algorithm, such as…
Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of…
Randomization procedures are used in legal and statistical applications, aiming to shield important decisions from spurious influences. This article gives an intuitive introduction to randomization and examines some intended consequences of…
Syndrome-based neural decoding (SBND) has emerged as a promising deep learning approach for soft-decision decoding of high-rate, short-length codes. However, this approach still has substantial room for improvement. In this paper, we show…
In this paper, we present a framework for generic decoding of convolutional codes, which allows us to do cryptanalysis of code-based systems that use convolutional codes. We then apply this framework to information set decoding, study…
We study a modification of Kendall's tau-test, replacing his permutations of n different numbers by sequences of length n, where repetition is allowed. In particular, binary sequences are included. Random sequences can be tested.
Random linear codes (RLCs) are well known to have nice combinatorial properties and near-optimal parameters in many different settings. However, getting explicit constructions matching the parameters of RLCs is challenging, and RLCs are…
We introduce style augmentation, a new form of data augmentation based on random style transfer, for improving the robustness of convolutional neural networks (CNN) over both classification and regression based tasks. During training, our…
In this paper we consider a transformation which converts uncorrelated networks to correlated ones(here by correlation we mean that coordination numbers of two neighbors are not independent). We show that this transformation, which converts…