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In this paper, we propose a coding scheme based on polar codes for empirical coordination of autonomous devices. We consider a two-node network with a noisy link in which the input and output signals have to be coordinated with the source…

Information Theory · Computer Science 2018-02-28 Giulia Cervia , Laura Luzzi , Maël Le Treust , Matthieu R. Bloch

Polar codes have been proven to be capacity achieving for any binary-input discrete memoryless channel, while at the same time they can reassure secure and reliable transmission over the single-input single-output wireless channel. However,…

The polarization decomposition of arbitrary binary-input memoryless channels (BMCs) is studied in this work. By introducing the polarization factor (PF), defined in terms of the conditional entropy of the channel output under various input…

Information Theory · Computer Science 2025-05-06 Tianfu Qi , Jun Wang

A generalization of Ar\i kan's polar code construction using transformations of the form $G^{\otimes n}$ where $G$ is an $\ell \times \ell$ matrix is considered. Necessary and sufficient conditions are given for these transformations to…

Information Theory · Computer Science 2008-11-12 Satish Babu Korada , Eren Sasoglu

The polar codes are proven to be capacity-achieving and are shown to have equivalent or even better finite-length performance than the turbo/LDPC codes under some improved decoding algorithms over the additive white Gaussian noise (AWGN)…

Information Theory · Computer Science 2014-05-20 Kai Chen , Kai Niu , Jiaru Lin

Polar codes, introduced by Arikan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error…

Information Theory · Computer Science 2010-07-22 Ryuhei Mori , Toshiyuki Tanaka

In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. This local-global construction is motivated by practical applications in data storage and transmission where reduced-latency…

Information Theory · Computer Science 2023-01-09 Ziyuan Zhu , Wei Wu , Paul H. Siegel

In this paper, we propose a novel partial order for binary discrete memoryless channels that we call the symmetric convex ordering. We show that Ar{\i}kan's polar transform preserves 'symmetric convex orders'. Furthermore, we show that…

Information Theory · Computer Science 2018-06-29 Mine Alsan

Polar codes provably achieve the symmetric capacity of a memoryless channel while having an explicit construction. This work aims to increase the throughput of polar decoder hardware by an order of magnitude relative to the state of the art…

Hardware Architecture · Computer Science 2015-05-20 Gabi Sarkis , Pascal Giard , Alexander Vardy , Claude Thibeault , Warren J. Gross

Product codes are widespread in optical communications, thanks to their high throughput and good error-correction performance. Systematic polar codes have been recently considered as component codes for product codes. In this paper, we…

Information Theory · Computer Science 2019-01-23 Valerio Bioglio , Carlo Condo , Ingmar Land

In this paper, we propose a comprehensive Polar coding solution that integrates reliability calculation, rate matching and parity-check coding. Judging a channel coding design from the industry's viewpoint, there are two primary concerns:…

Information Theory · Computer Science 2018-01-12 Huazi Zhang , Rong Li , Jian Wang , Shengchen Dai , Gongzheng Zhang , Ying Chen , Hejia Luo , Jun Wang

Polar codes, discovered by Ar{\i}kan, are the first error-correcting codes with an explicit construction to provably achieve channel capacity, asymptotically. However, their error-correction performance at finite lengths tends to be lower…

Information Theory · Computer Science 2015-06-16 Alexandre J. Raymond , Warren J. Gross

A framework is proposed that allows for a joint description and optimization of both binary polar coding and $2^m$-ary digital pulse-amplitude modulation (PAM) schemes such as multilevel coding (MLC) and bit-interleaved coded modulation…

Information Theory · Computer Science 2013-02-13 Mathis Seidl , Andreas Schenk , Clemens Stierstorfer , Johannes B. Huber

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Ar{\i}kan style constructions. This paper, which is presented in two…

Information Theory · Computer Science 2017-02-07 Rajai Nasser

When a neural network (NN) is used to decode a polar code, its training complexity scales exponentially as the code block size (or to be precise, as a number of message bits) increases. Therefore, existing solutions that use a neural…

Information Theory · Computer Science 2022-11-10 Evgeny Stupachenko

In this paper, we study the connection between polar codes and product codes. Our analysis shows that the product of two polar codes is again a polar code, and we provide guidelines to compute its frozen set on the basis of the frozen sets…

Information Theory · Computer Science 2020-04-22 Carlo Condo , Valerio Bioglio , Hartmut Hafermann , Ingmar Land

In 1948, Shannon used a probabilistic argument to show the existence of codes achieving a maximal rate defined by the channel capacity. In 1954, Muller and Reed introduced a simple deterministic code construction based on polynomial…

Information Theory · Computer Science 2026-02-26 Emmanuel Abbe , Colin Sandon , Vladyslav Shashkov , Maryna Viazovska

We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding…

Information Theory · Computer Science 2010-09-27 Mattias Andersson , Vishwambhar Rathi , Ragnar Thobaben , Joerg Kliewer , Mikael Skoglund

Being attracted by the property of classical polar code, researchers are trying to find its analogue in quantum fields, which is called quantum polar code. The first step and the key to design quantum polar code is to find out for the…

Quantum Physics · Physics 2022-03-25 Zhengzhong Yi , Zhipeng Liang , Xuan Wang

Polar codes are considered the latest major breakthrough in coding theory. Polar codes were introduced by Ar{\i}kan in 2008. In this letter, we show that the binary polar codes are the same as the optimized codes for bitwise multistage…

Information Theory · Computer Science 2016-04-14 Mostafa El-Khamy , Hsien-Ping Lin , Jungwon Lee