Related papers: Systematic Error-Correcting Codes for Rank Modulat…
Cyclic redundancy check (CRC) codes check if a codeword is correctly received. This paper presents an algorithm to design CRC codes that are optimized for the code-specific error behavior of a specified feedforward convolutional code. The…
Exact-repair regenerating codes are considered for the case (n,k,d)=(4,3,3), for which a complete characterization of the rate region is provided. This characterization answers in the affirmative the open question whether there exists a…
Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that…
The problem of securing a network coding communication system against an eavesdropper adversary is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the adversary can eavesdrop…
Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information storage and transmission. We report the implementation of a concatenated quantum error-correcting code able to correct…
An algorithm of improving the performance of iterative decoding on perpendicular magnetic recording is presented. This algorithm follows on the authors' previous works on the parallel and serial concatenated turbo codes and low-density…
Click data collected by modern recommendation systems are an important source of observational data that can be utilized to train learning-to-rank (LTR) systems. However, these data suffer from a number of biases that can result in poor…
Shannon's seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on theoretical neuroscience, ideas from mathematical coding…
Evaluation metrics play a vital role in the growth of an area as it defines the standard of distinguishing between good and bad models. In the area of code synthesis, the commonly used evaluation metric is BLEU or perfect accuracy, but they…
We construct an explicit family of linear rank-metric codes over any field ${\mathbb F}_h$ that enables efficient list decoding up to a fraction $\rho$ of errors in the rank metric with a rate of $1-\rho-\epsilon$, for any desired $\rho \in…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…
We introduce synchronization strings as a novel way of efficiently dealing with synchronization errors, i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to deal with than commonly considered…
New bounds on classification error rates for the error-correcting output code (ECOC) approach in machine learning are presented. These bounds have exponential decay complexity with respect to codeword length and theoretically validate the…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
Progress in neural grammatical error correction (GEC) is hindered by the lack of annotated training data. Sufficient amounts of high-quality manually annotated data are not available, so recent research has relied on generating synthetic…
Just as rank-metric or Gabidulin codes may be used to construct rate-diversity tradeoff optimal space-time codes, a recently introduced generalization for the sum-rank metric -- linearized Reed-Solomon codes -- accomplishes the same in the…
Is perfect error correction always worth the trouble? A framework is presented for the analysis of error detection and correction in multi-level systems of communication that takes into account degrees of freedom attended and ignored by…
Quantum error correction will likely be essential for building a large-scale quantum computer, but it comes with significant requirements at the level of classical control software. In particular, a quantum error-correcting code must be…
A recent landscape analysis of LoRA fine-tuning in the neural tangent kernel regime establishes a sufficient condition $r(r+1)/2 > KN$ on the LoRA rank $r$ for the absence of spurious local minima under squared-error loss, prescribing $r…