Related papers: Recursive Decoding and Its Performance for Low-Rat…
We construct $s$-interleaved linearized Reed--Solomon (ILRS) codes and variants and propose efficient decoding schemes that can correct errors beyond the unique decoding radius in the sum-rank metric. The proposed interpolation-based scheme…
The main decoding algorithms for Reed-Solomon codes are based on a bivariate interpolation step, which is expensive in time complexity. Lot of interpolation methods were proposed in order to decrease the complexity of this procedure, but…
Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…
Codes in the sum-rank metric have various applications in error control for multishot network coding, distributed storage and code-based cryptography. Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as…
Large Multimodal Models (LMMs) have achieved remarkable success in vision-language tasks, yet their vast parameter counts are often underutilized during both training and inference. In this work, we embrace the idea of looping back to move…
We define and study a class of Reed-Muller type error-correcting codes obtained from elementary symmetric functions in finitely many variables. We determine the code parameters and higher weight spectra in the simplest cases.
Recurrent neural networks have proved to be an effective method for statistical language modeling. However, in practice their memory and run-time complexity are usually too large to be implemented in real-time offline mobile applications.…
Errors in surface code have typically been decoded by Minimum Weight Perfect Matching (MWPM) based method. Recently, neural-network-based Machine Learning (ML) techniques have been employed for this purpose. Here we propose a two-level (low…
In this paper we devise a rational curve fitting algorithm and apply it to the list decoding of Reed-Solomon and BCH codes. The proposed list decoding algorithms exhibit the following significant properties. 1 The algorithm corrects up to…
Binary decompilation is a critical reverse engineering task aimed at reconstructing high-level source code from stripped executables. Although Large Language Models (LLMs) have recently shown promise, they often suffer from "logical…
Folded Reed-Solomon (FRS) and univariate multiplicity codes are prominent polynomial codes over finite fields, renowned for achieving list decoding capacity. These codes have found a wide range of applications beyond the traditional scope…
We improve the method in \cite{Seidl:10} for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known…
This paper considers '$\delta$-almost Reed-Muller codes', i.e., linear codes spanned by evaluations of all but a $\delta$ fraction of monomials of degree at most $d$. It is shown that for any $\delta > 0$ and any $\varepsilon>0$, there…
We investigate the computational complexity of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages. We focus on the single-layer, ReLU-activation, rational-weight RNNs with…
We propose a new algorithm for decoding Reed-Solomon codes (up to half the minimum distance) and for computing inverses in $F[x]/m(x)$. The proposed algorithm is similar in spirit and structure to the Berlekamp-Massey algorithm, but it…
With the advent of neural language models, the performance of code generation has been significantly boosted. However, the problem of repetitions during the generation process continues to linger. Previous work has primarily focused on…
We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known…
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…
We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code…
We propose a data-driven approach to explicitly learn the progressive encoding of a continuous source, which is successively decoded with increasing levels of quality and with the aid of correlated side information. This setup refers to the…