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Iterative Refinement (IR) is a classical computing technique for obtaining highly precise solutions to linear systems of equations, as well as linear optimization problems. In this paper, motivated by the limited precision of quantum…

Optimization and Control · Mathematics 2023-12-19 Mohammadhossein Mohammadisiahroudi , Brandon Augustino , Pouya Sampourmahani , Tamás Terlaky

Polar codes are widely used in modern communication systems due to their capacity-achieving properties. This paper investigates the importance of coded bits in the decoding process of polar codes and aims to determine which bits contribute…

Information Theory · Computer Science 2025-07-14 Hossam Hassan , Ali Gaber , Mohammed Karmoose , Noha Korany

We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…

Quantum Physics · Physics 2009-11-13 David Poulin

Achieving information-theoretic security using explicit coding scheme in which unlimited computational power for eavesdropper is assumed, is one of the main topics is security consideration. It is shown that polar codes are capacity…

We propose a novel binary polarization shift keying modulation scheme for a line-of-sight environment by exploiting the polarization control ability of the reconfigurable intelligent surface (RIS). The RIS encodes the information data in…

Information Theory · Computer Science 2021-12-16 Emad Ibrahim , Rickard Nilsson , Jaap van de Beek

A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar…

Information Theory · Computer Science 2013-02-04 Hessam Mahdavifar , Mostafa El-Khamy , Jungwon Lee , Inyup Kang

In successive cancellation (SC) polar decoding, an incorrect estimate of any prior unfrozen bit may bring about severe error propagation in the following decoding, thus it is desirable to find out and correct an error as early as possible.…

Information Theory · Computer Science 2017-12-12 Zhaoyang Zhang , Kangjian Qin , Liang Zhang , Huazi Zhang , Guo Tai Chen

In the conventional successive cancellation (SC) decoder for polar codes, all the future bits to be estimated later are treated as random variables. However, polar codes inevitably involve frozen bits, and their concatenated coding schemes…

Information Theory · Computer Science 2023-09-19 Min Jang , Jong-Hwan Kim , Seho Myung , Kyeongcheol Yang

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…

Information Theory · Computer Science 2016-11-17 Hessam Mahdavifar , Mostafa El-Khamy , Jungwon Lee , Inyup Kang

Long polar codes can achieve the capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancelation (SC) decoding algorithm. But for polar codes with short and moderate code length, the decoding…

Information Theory · Computer Science 2016-11-18 Jun Lin , Chenrong Xiong , Zhiyuan Yan

This paper presents an enhanced belief propagation (BP) decoding algorithm and a reinforcement learning-based BP decoding algorithm for polar codes. The enhanced BP algorithm weighs each Processing Element (PE) input based on their signals…

Information Theory · Computer Science 2021-11-02 L. M. Oliveira , R. M. Oliveira , R. C. de Lamare

Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of…

In Private Information Retrieval (PIR), one wants to download a file from a database without revealing to the database which file is being downloaded. Much attention has been paid to the case of the database being encoded across several…

Information Theory · Computer Science 2017-06-23 Razane Tajeddine , Oliver W. Gnilke , David Karpuk , Ragnar Freij-Hollanti , Camilla Hollanti , Salim El Rouayheb

Due to the ability to provide superior error-correction performance, the successive cancellation list (SCL) algorithm is widely regarded as one of the most promising decoding algorithms for polar codes with short-to-moderate code lengths.…

Information Theory · Computer Science 2023-11-15 Yang Lu , Ming-Min Zhao , Ming Lei , Min-Jian Zhao

We present two polarization-based protocols for quantum key distribution. The protocols encode key bits in noiseless subspaces or subsystems, and so can function over a quantum channel subjected to an arbitrary degree of collective noise,…

Quantum Physics · Physics 2009-11-10 J. -C. Boileau , D. Gottesman , R. Laflamme , D. Poulin , R. W. Spekkens

This work presents a fast successive-cancellation list flip (Fast-SCLF) decoding algorithm for polar codes that addresses the high latency issue associated with the successive-cancellation list flip (SCLF) decoding algorithm. We first…

Information Theory · Computer Science 2022-01-25 Nghia Doan , Seyyed Ali Hashemi , Warren J. Gross

Intensive work on quantum computing has increased interest in quantum cryptography in recent years. Although this technique is characterized by a very high level of security, there are still challenges that limit the widespread use of…

Cryptography and Security · Computer Science 2019-04-30 Marcin Niemiec

Polar codes can theoretically achieve very competitive Frame Error Rates. In practice, their performance may depend on the chosen decoding procedure, as well as other parameters of the communication system they are deployed upon. As a…

Machine Learning · Computer Science 2021-05-12 Mathieu Léonardon , Vincent Gripon

Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error…

Quantum Physics · Physics 2018-12-05 A. Bolt , D. Poulin , T. M. Stace

Targeting high-throughput and low-power communications, we implement two successive cancellation (SC) decoders for polar codes. With $16nm$ ASIC technology, the area efficiency and energy efficiency are $4Tbps/mm^2$ and $0.63pJ/bit$,…

Information Theory · Computer Science 2021-07-20 Jiajie Tong , Xianbin Wang , Qifan Zhang , Huazi Zhang , Rong Li , Jun Wang , Wen Tong