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The new method for Reed-Solomon codes decoding is introduced. The method is based on the star trellis decoding of the binary image of Reed-Solomon codes.
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…
We show that the known list-decoding algorithms for univariate multiplicity and folded Reed-Solomon codes can be made to run in $\tilde{O}(n)$ time. Univariate multiplicity codes and FRS codes are natural variants of Reed-Solomon codes that…
Recently, a new polynomial basis over binary extension fields was proposed such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order $\mathcal{O}(n\lg(n))$, where $n$ is the number of points…
Skew polynomials are a class of non-commutative polynomials that have several applications in computer science, coding theory and cryptography. In particular, skew polynomials can be used to construct and decode evaluation codes in several…
Analysis of the Berlekamp-Massey-Sakata algorithm for decoding one-point codes leads to two methods for improving code rate. One method, due to Feng and Rao, removes parity checks that may be recovered by their majority voting algorithm.…
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust…
Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…
Quantum communication technologies will play an important role in quantum information processing in the near future as we network devices together. However, their implementation is still a challenging task due to both loss and gate errors.…
A fast implementation of the OPED algorithm, a reconstruction algorithm for Radon data introduced recently, is proposed and tested. The new implementation uses FFT for discrete sine transform and an interpolation step. The convergence of…
Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the…
A new interpolation-based decoding principle for interleaved Gabidulin codes is presented. The approach consists of two steps: First, a multi-variate linearized polynomial is constructed which interpolates the coefficients of the received…
We survey the known list decoding algorithms for polar codes and compare their complexity. Index terms: Polar codes; Reed-Muller codes; successive cancellation decoding.
Reed-Muller codes are some of the oldest and most widely studied error-correcting codes, of interest for both their algebraic structure as well as their many algorithmic properties. A recent beautiful result of Saptharishi, Shpilka and Volk…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
Coded computing has emerged as a key framework for addressing the impact of stragglers in distributed computation. While polynomial functions often admit exact recovery under existing coded computing schemes, non-polynomial functions…
In this paper we provide a detailed description of Reed-Solomon (RS) codes, the most important algorithms for decoding them, and their use in concatenated coding systems for space applications. In the current literature there is scattered…
Good quantum error-correcting codes that fulfill practical considerations, such as simple encoding circuits and efficient decoders, are essential for functional quantum information processing systems. Quantum polar codes satisfy some of…
We demonstrate that the method of interleaved resampling in the context of parton showers can tremendously improve the statistical convergence of weighted parton shower evolution algorithms. We illustrate this by several examples showing…
A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation…