Concept

Code de Golay

Publications associées (41)

The beginning of 21st century provided us with many answers about how to reach the channel capacity. Polarization and spatial coupling are two techniques for achieving the capacity of binary memoryless symmetric channels under low-complexity decoding algor ...

EPFL2022

On the Efficiency of Polar-Like Decoding for Symmetric Codes

Rüdiger Urbanke, Kirill Ivanov

The recently introduced polar codes constitute a breakthrough in coding theory due to their capacity-achieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures based on the Plo ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Edge-based and face-based smoothed finite element methods (ES-FEM and FS-FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear eleme ...

WILEY2022

Almost impossible E_8 and Leech lattices

Maryna Viazovska

We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...

2021

On Codes Decoding a Constant Fraction of Errors on the BSC

Jan Hazla

We strengthen the results from a recent work by the second author, achieving bounds on the weight distribution of binary linear codes that are successful under block-MAP (as well as bit-MAP) decoding on the BEC. We conclude that a linear code that is succe ...

ASSOC COMPUTING MACHINERY2021

New Results On The Pseudoredundancy

Zihui Liu

The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding ...

2019

On the Computational Complexity of Blind Detection of Binary Linear Codes

Alexios Konstantinos Balatsoukas Stimming, Aris Filos Ratsikas

In this work, we study the computational complexity of the Minimum Distance Code Detection problem. In this problem, we are given a set of noisy codeword observations and we wish to find a code in a set of linear codes C of a given dimension k, for which t ...

IEEE2019

Improved decoding of second-order Reed-Muller codes

Rüdiger Urbanke, Kirill Ivanov

In this paper, we consider low-complexity decoding of second-order Reed-Muller codes. A class of polynomial-time algorithms, based on the projections onto first-order codes, is studied. An old representative of this class, originally developed for binary s ...

IEEE2019

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The performance of unipolar unicolor coded Brillouin optical time-domain analysis (BOTDA) is evaluated based on both Simplex and Golay codes. Four major detrimental factors that limit the system performance, including decoded-gain trace distortion, coding ...

2018

Almost Optimal Scaling of Reed-Muller Codes on BEC and BSC Channels

Rüdiger Urbanke, Seyed Hamed Hassani, Shrinivas Kudekar, Yury Polyanskiy

Consider a binary linear code of length N, minimum distance d(min), transmission over the binary erasure channel with parameter 0 < epsilon < 1 or the binary symmetric channel with parameter 0 < epsilon < 1/2, and block-MAP decoding. It was shown by Tillic ...

IEEE2018

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