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In this paper, we establish the partial order (POs) for both the binary erasure channel (BEC) and the binary memoryless symmetric channel (BMSC) under any block rate-matched polar codes. Firstly, we define the POs in the sense of…

信息论 · 计算机科学 2024-11-07 Zhichao Liu , Liuquan Yao , Yuan Li , Huazi Zhang , Jun Wang , Guiying Yan , Zhiming Ma

We consider explicit polar constructions of blocklength $n\rightarrow\infty$ for the two extreme cases of code rates $R\rightarrow1$ and $R\rightarrow0.$ For code rates $R\rightarrow1,$ we design codes with complexity order of $n\log n$ in…

信息论 · 计算机科学 2017-02-17 Ilya Dumer

In this paper, we study polar codes from a practical point of view. In particular, we study concatenated polar codes and rate-compatible polar codes. First, we propose a concatenation scheme including polar codes and Low-Density…

信息论 · 计算机科学 2011-07-28 Ali Eslami , Hossein Pishro-Nik

Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the corresponding code length is limited to the power of two. In this paper, we establish a…

信息论 · 计算机科学 2017-12-05 Kai Niu , Jincheng Dai , Kai Chen , Jiaru Lin , Q. T. Zhang , Athanasios V. Vasilakos

We consider the problem of polar coding for transmission over $m$-user multiple access channels. In the proposed scheme, all users encode their messages using a polar encoder, while a joint successive cancellation decoder is deployed at the…

信息论 · 计算机科学 2016-11-17 Hessam Mahdavifar , Mostafa El-Khamy , Jungwon Lee , Inyup Kang

Polar codes has been selected as 5G standard. However, only a couple of ASIC featuring decoders are fabricated,and none of them support list size L > 4 and code length N > 1024. This paper presents an ASIC implementation of three decoders…

信息论 · 计算机科学 2018-07-05 Xiaocheng Liu , Qifan Zhang , Pengcheng Qiu , Jiajie Tong , Huazi Zhang , Changyong Zhao , Jun Wang

In this work, we present hardware and software implementations of flexible polar systematic encoders and decoders. The proposed implementations operate on polar codes of any length less than a maximum and of any rate. We describe the…

信息论 · 计算机科学 2016-08-29 Gabi Sarkis , Ido Tal , Pascal Giard , Alexander Vardy , Claude Thibeault , Warren J. Gross

We propose a new polar code construction framework (i.e., selecting the frozen bit positions) for the additive white Gaussian noise (AWGN) channel, tailored to a given decoding algorithm, rather than based on the (not necessarily optimal)…

信息论 · 计算机科学 2019-01-23 Ahmed Elkelesh , Moustafa Ebada , Sebastian Cammerer , Stephan ten Brink

A hybrid automatic repeat request scheme with Chase combing (HARQ-CC) of polar codes is proposed. The existing analysis tools of the underlying rate-compatible punctured polar (RCPP) codes for additive white Gaussian noise (AWGN) channels…

信息论 · 计算机科学 2014-01-13 Kai Chen , Kai Niu , Zhiqiang He , Jiaru Lin

Polar-coded multiple-input multiple-output systems are investigated. An advanced receiver implementing joint list decoding of polar codes and QR- and MMSE-based detectors is proposed. The approximate and exact path metrics are derived for…

信息论 · 计算机科学 2025-08-29 Liudmila Karakchieva , Peter Trifonov

A novel structure of polar codes is proposed for finite-state modulation (FSM), in order to improve polarization under it, and approach the polarization efficiency that conventional polar codes achieve under memoryless channels. We choose a…

信息论 · 计算机科学 2025-07-08 Yinuo Mei , Yangyong Zhang , Daiming Qu

In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity $\frac{1}{2}\log(1+\SNR)$ of the additive white Gaussian-noise (AWGN) channel. Our construction follows the…

信息论 · 计算机科学 2018-10-16 Ling Liu , Yanfei Yan , Cong Ling , Xiaofu Wu

Polar codes are the first error-correcting code proven to achieve channel capacity based on infinite code length. The Successive Cancellation List Flip (SCLF) decoding algorithm was proposed by flipping an erroneous bit during the next…

信号处理 · 电气工程与系统科学 2026-05-25 Fu-Siang Liang , Shan Lu , Yeong-Luh Ueng

Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while…

信息论 · 计算机科学 2015-04-15 Naveen Goela , Emmanuel Abbe , Michael Gastpar

Row-merged polar codes are a family of pre-transformed polar codes (PTPCs) with little precoding overhead. Providing an improved distance spectrum over plain polar codes, they are capable to perform close to the finite-length capacity…

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)…

信息论 · 计算机科学 2014-05-20 Kai Chen , Kai Niu , Jiaru Lin

Recently, a novel variation of polar codes known as polarization-adjusted convolutional (PAC) codes has been introduced by Ar{\i}kan. These codes significantly outperform conventional polar and convolutional codes, particularly for short…

信息论 · 计算机科学 2025-08-15 Mohsen Moradi , Hessam Mahdavifar

Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error…

信息论 · 计算机科学 2021-08-11 Kai Niu , Yan Li

In this paper, we introduce a novel class of pre-transformed polar codes, termed as deep polar codes. We first present a deep polar encoder that harnesses a series of multi-layered polar transformations with varying sizes. Our approach to…

信息论 · 计算机科学 2023-08-08 Geon Choi , Namyoon Lee

With the evolution from 5G to 6G, ultra-reliable low-latency communication (URLLC) faces increasingly stringent performance requirements. Lower latency constraints demand shorter channel coding lengths, which can severely degrade decoding…

信息论 · 计算机科学 2025-08-07 Yaqi Li , Xiaohu You , Jiamin Li , Chen Ji , Bin Sheng