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We study LDPC codes for the channel with $2^m$-ary input $\underline{x}\in \mathbb{F}_2^m$ and output $\underline{y}=\underline{x}+\underline{z}\in \mathbb{F}_2^m$. The receiver knows a subspace $V\subset \mathbb{F}_2^m$ from which…

Information Theory · Computer Science 2012-05-22 Kenta Kasai , Takayuki Nozaki , Kohichi Sakaniwa

The iterative decoding threshold of low-density parity-check (LDPC) codes over the binary erasure channel (BEC) fulfills an upper bound depending only on the variable and check nodes with minimum distance 2. This bound is a consequence of…

Information Theory · Computer Science 2010-07-28 Enrico Paolini , Marc Fossorier , Marco Chiani

For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at…

Information Theory · Computer Science 2016-11-17 Arunkumar Subramanian , Andrew Thangaraj , Matthieu Bloch , Steven W. McLaughlin

Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information maximizing lookup tables replace the conventional operations of the…

Information Theory · Computer Science 2019-10-24 Maximilian Stark , Jan Lewandowsky , Souradip Saha , Gerhard Bauch

Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…

Information Theory · Computer Science 2022-04-15 Samet Gelincik , Philippe Mary , Anne Savard , Jean-Yves Baudais

We obtain exact expressions for the asymptotic behaviour of the average probability of the block decoding error for ensembles of regular low density parity check error correcting codes, by employing diagrammatic techniques. Furthermore, we…

Statistical Mechanics · Physics 2007-05-23 J. van Mourik , Y. Kabashima

One approach to designing structured low-density parity-check (LDPC) codes with large girth is to shorten codes with small girth in such a manner that the deleted columns of the parity-check matrix contain all the variables involved in…

Discrete Mathematics · Computer Science 2016-11-18 Olgica Milenkovic , Navin Kashyap , David Leyba

Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…

Information Theory · Computer Science 2018-04-30 Elia Santi , Christian Häger , Henry D. Pfister

An efficient scheme to increase the performance of polar codes at short and moderate block lengths is a concatenation of CRC code and a polar code. In order to obtain better result of the concatenation, a CRC code with best error control…

Information Theory · Computer Science 2019-12-17 Tsonka Baicheva , Peter Kazakov

A new approach for combining non-binary low-density parity-check (NB-LDPC) codes with higher-order modulation and probabilistic amplitude shaping (PAS) is presented. Instead of symbol-metric decoding (SMD), a bit-metric decoder (BMD) is…

Information Theory · Computer Science 2018-09-12 Fabian Steiner , Georg Böcherer , Gianluigi Liva

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

Low-density parity-check (LPDC) decoders assume the channel estate information (CSI) is known and they have the true a posteriori probability (APP) for each transmitted bit. But in most cases of interest, the CSI needs to be estimated with…

Information Theory · Computer Science 2010-06-07 Luis Salamanca , Juan José Murillo-Fuentes , Fernando Pérez-Cruz

This work identifies information-theoretic quantities that are closely related to the required list size on average for successive cancellation list (SCL) decoding to implement maximum-likelihood decoding over general binary memoryless…

Information Theory · Computer Science 2022-04-04 Mustafa Cemil Coşkun , Henry D. Pfister

For a multiple-input multiple-output (MIMO) system with unknown channel state information (CSI), a novel low-density parity check (LDPC)-coded transmission (LCT) scheme with joint pilot and data channel estimation is proposed. To fine-tune…

Information Theory · Computer Science 2023-11-14 Binghui Shi , Yongpeng Wu , Peihong Yuan , Derrick Wing Kwan Ng , Xiang-Gen Xia , Wenjun Zhang

This work shows how non-binary low-density parity-check codes over GF($2^p$) can be combined with probabilistic amplitude shaping (PAS) (B\"ocherer, et al., 2015), which combines forward-error correction with non-uniform signaling for…

Information Theory · Computer Science 2017-08-21 Fabian Steiner , Gianluigi Liva , Georg Böcherer

For improving coarsely quantized decoding of LDPC codes, we propose a check node aware design of the variable node update. In contrast to previous works, we optimize the variable node to explicitly maximize the mutual information preserved…

Information Theory · Computer Science 2022-11-15 Philipp Mohr , Gerhard Bauch

Polar codes have been adopted as the control channel coding scheme in the fifth generation new radio (5G NR) standard due to its capacity-achievable property. Traditional polar decoding algorithms such as successive cancellation (SC) suffer…

Signal Processing · Electrical Eng. & Systems 2019-08-02 Zhiwei Cao , Hongfei Zhu , Yuping Zhao , Dou Li

In this paper, we present a construction method of non-binary low-density parity-check (LDPC) convolutional codes. Our construction method is an extension of Felstroem and Zigangirov construction for non-binary LDPC convolutional codes. The…

Information Theory · Computer Science 2015-05-20 Hironori Uchikawa , Kenta Kasai , Kohichi Sakaniwa

We propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy…

Quantum Physics · Physics 2025-12-18 Min Ye , Dave Wecker , Nicolas Delfosse

We propose a new type of ultimate-Shannon-limit-approaching codes called spatially coupled protograph-based low-density parity-check Hadamard convolutional codes (SC-PLDPCH-CCs), which are constructed by spatially coupling PLDPC-Hadamard…

Information Theory · Computer Science 2022-07-26 Peng W. Zhang , Francis C. M. Lau , Chiu-W. Sham