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Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based…

Information Theory · Computer Science 2009-09-04 Jose Ignacio Iglesias Curto , Uwe Helmke

Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest. While they are provably capacity achieving over various channels, they have seen limited practical applications.…

Information Theory · Computer Science 2016-11-17 Alexios Balatsoukas-Stimming , Georgios Karakonstantis , Andreas Burg

Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…

Logic in Computer Science · Computer Science 2016-07-18 Peter Schrammel

This paper proposes a concise coding of the cells of n-dimensional finite regular grids. It induces a simple, generic and efficient framework for implementing classical digital topology data structures and algorithms. Discrete subsets of…

Discrete Mathematics · Computer Science 2009-06-16 Jacques-Olivier Lachaud

In this research, we propose a deep learning based approach for speeding up the topology optimization methods. The problem we seek to solve is the layout problem. The main novelty of this work is to state the problem as an image…

Machine Learning · Computer Science 2017-09-28 Ivan Sosnovik , Ivan Oseledets

It is proposed a new code for contours of plane images. This code was applied for optical character recognition of printed and handwritten characters. One can apply it to recognition of any visual images.

Computer Vision and Pattern Recognition · Computer Science 2012-12-05 Evgeny Shchepin

We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight…

Quantum Physics · Physics 2022-10-26 Anthony Leverrier , Gilles Zémor

Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…

Quantum Physics · Physics 2024-02-02 Yugo Takada , Yusaku Takeuchi , Keisuke Fujii

A reduced complexity sequential decoding algorithm for polar (sub)codes is described. The proposed approach relies on a decomposition of the polar (sub)code being decoded into a number of outer codes, and on-demand construction of codewords…

Information Theory · Computer Science 2020-07-08 Grigorii Trofimiuk , Nikolay Iakuba , Stanislav Rets , Kirill Ivanov , Peter Trifonov

The color code is remarkable for its ability to perform fault-tolerant logic gates. This motivates the design of practical decoders that minimise the resource cost of color-code quantum computation. Here we propose a decoder for the planar…

Quantum Physics · Physics 2022-01-20 Kaavya Sahay , Benjamin J. Brown

An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…

Information Theory · Computer Science 2009-01-23 In Sook Park

An efficient implementation of min-sum SC/list decoding of convolutional polar codes is proposed. The complexity of the proposed implementation of SC decoding is more than two times smaller than the straightforward implementation. Moreover,…

Information Theory · Computer Science 2020-07-14 Ruslan Morozov

An implementation-efficient finite alphabet decoder for polar codes relying on coarsely quantized messages and low-complexity operations is proposed. Typically, finite alphabet decoding performs concatenated compression operations on the…

Information Theory · Computer Science 2023-05-29 Philipp Mohr , Syed Aizaz Ali Shah , Gerhard Bauch

Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity. Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where…

Information Theory · Computer Science 2016-07-12 Pascal Giard , Gabi Sarkis , Camille Leroux , Claude Thibeault , Warren J. Gross

Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine…

Quantum Physics · Physics 2020-11-04 Thomas Wagner , Hermann Kampermann , Dagmar Bruß

We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…

Information Theory · Computer Science 2016-11-18 Alex Yufit , Asi Lifshitz , Yair Be'ery

Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code. Using such circuits for the surface code requires decoding…

Quantum Physics · Physics 2026-02-23 Marc Serra-Peralta , Mackenzie H. Shaw , Barbara M. Terhal

We describe a successive-cancellation \emph{list} decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Ar{\i}kan. In the proposed list decoder, up to $L$ decoding paths are considered…

Information Theory · Computer Science 2012-06-04 Ido Tal , Alexander Vardy

The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…

Numerical Analysis · Mathematics 2016-10-20 Sergey Voronin , Per-Gunnar Martinsson

In this paper we investigate the decoding of parallel turbo codes over the binary erasure channel suited for upper-layer error correction. The proposed algorithm performs on-the-fly decoding, i.e. it starts decoding as soon as the first…

Information Theory · Computer Science 2008-03-13 Ghassan M. Kraidy , Valentin Savin