A class of good quasi-cyclic low-density parity check codes based on progressive edge growth graph

Li, Zongwang; Kumar, B. V. K. Vijaya

doi:10.1109/acssc.2004.1399513

Cited by 79 publications

(11 citation statements)

References 11 publications

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“…Future efforts could lead to a choice of a vastly different code as a basis for comparison, e.g. an irregular LDPC code with different code rate and dimensions or to the application of methods from [13][14][15][16][17][18] to construct QC-LDPC codes using the algorithms described in this paper. These structured codes would be better suited for hardware implementation.…”

Section: Discussion Of the Research Results Of Ldpc Construction And Performance-enhancing Algorithmsmentioning

confidence: 99%

“…This structure lowers their complexity and makes them much more hardware-friendly. Although PEG LDPC codes themselves are often impractical for hardware implementations, there exist several methods for construction of QC-LDPC codes with the use of the PEG algorithm (while retaining the advantages of QC-LDPC codes) [13][14][15][16][17][18], e. g. by generating each submatrix of the final parity-check matrix using the PEG algorithm. In [13], the construction of PEG-QC-LDPC codes (type of LDPC codes with the advantage of lower memory requirements) than PEG codes is described together with modifications to also maximize its girth properties.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…The authors state that this is a unique approach because they have not found any similar publications which focus on these channel conditions. The paper [16] contains methods for constructing both regular and irregular quasi-cyclic LDPC codes with error-correcting benefits of progressive edge-growth codes. The authors state that their proposed codes exhibit BER performance comparable to random-structure LDPC codes.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Investigation of random-structure regular LDPC codes construction based on progressive edge-growth and algorithms for removal of short cycles

Durcek

Kuba

Dado

2021

EEJET

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This paper investigates the construction of random-structure LDPC (low-density parity-check) codes using Progressive Edge-Growth (PEG) algorithm and two proposed algorithms for removing short cycles (CB1 and CB2 algorithm; CB stands for Cycle Break). Progressive Edge-Growth is an algorithm for computer-based design of random-structure LDPC codes, the role of which is to generate a Tanner graph (a bipartite graph, which represents a parity-check matrix of an error-correcting channel code) with as few short cycles as possible. Short cycles, especially the shortest ones with a length of 4 edges, in Tanner graphs of LDPC codes can degrade the performance of their decoding algorithm, because after certain number of decoding iterations, the information sent through its edges is no longer independent. The main contribution of this paper is the unique approach to the process of removing short cycles in the form of CB2 algorithm, which erases edges from the code's parity-check matrix without decreasing the minimum Hamming distance of the code. The two cycle-removing algorithms can be used to improve the error-correcting performance of PEG-generated (or any other) LDPC codes and achieved results are provided. All these algorithms were used to create a PEG LDPC code which rivals the best-known PEG-generated LDPC code with similar parameters provided by one of the founders of LDPC codes. The methods for generating the mentioned error-correcting codes are described along with simulations which compare the error-correcting performance of the original codes generated by the PEG algorithm, the PEG codes processed by either CB1 or CB2 algorithm and also external PEG code published by one of the founders of LDPC codes

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Section: Discussion Of the Research Results Of Ldpc Construction And Performance-enhancing Algorithmsmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Investigation of random-structure regular LDPC codes construction based on progressive edge-growth and algorithms for removal of short cycles

Durcek

Kuba

Dado

2021

EEJET

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“…Many of the construction techniques have been adopted in the construction of quantum LDPC codes, e.g., [239]- [242]. Furthermore, the PEG algorithm may be effectively used to construct QC-LDPC codes by adding randomness to the code design, e.g., [243]- [245]. In practice, a QC-LDPC code is often designed using a hybrid of the two approaches so that the optimized pseudorandom construction performs well in the waterfall region, while code structure can help provide exemplary performance in the error floor region.…”

Section: Finite-length Construction Of Qc-ldpc Codesmentioning

confidence: 99%

Channel Coding Toward 6G: Technical Overview and Outlook

Rowshan,

Qiu,

Xie

et al. 2024

IEEE Open J. Commun. Soc.

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Channel coding plays a pivotal role in ensuring reliable communication over wireless channels. With the growing need for ultra-reliable communication in emerging wireless use cases, the significance of channel coding has amplified. Furthermore, minimizing decoding latency is crucial for critical-mission applications, while optimizing energy efficiency is paramount for mobile and the Internet of Things (IoT) communications. As the fifth generation (5G) of mobile communications is currently in operation and 5G-advanced is on the horizon, the objective of this paper is to assess prominent channel coding schemes in the context of recent advancements and the anticipated requirements for the sixth generation (6G). In this paper, after considering the potential impact of channel coding on key performance indicators (KPIs) of wireless networks, we review the evolution of mobile communication standards and the organizations involved in the standardization, from the first generation (1G) to the current 5G, highlighting the technologies integral to achieving targeted KPIs such as reliability, data rate, latency, energy efficiency, spectral efficiency, connection density, and traffic capacity. Following this, we delve into the anticipated requirements for potential use cases in 6G. The subsequent sections of the paper focus on a comprehensive review of three primary coding schemes utilized in past generations and their recent advancements: lowdensity parity-check (LDPC) codes, turbo codes (including convolutional codes), and polar codes (alongside Reed-Muller codes). Additionally, we examine alternative coding schemes like Fountain codes (also known as rate-less codes), sparse regression codes, among others. Our evaluation includes a comparative analysis of error correction performance and the performance of hardware implementation for these coding schemes, providing insights into their potential and suitability for the upcoming 6G era. Lastly, we will briefly explore considerations such as higher-order modulations and waveform design, examining their contributions to enhancing key performance indicators in conjunction with channel coding schemes.

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“…In addition, modified PEG-construction with lineartime encoding can be achieved without noticeable performance degradation, facilitating the design of linear time encodable tensor product codes. Of the two approaches to achieve linear time encodability, namely, the upper triangular parity check matrix construction [30] and PEG construction with a QC constraint [31], we choose the latter approach, for which the designed codes have better error floor behavior. T-EPCC-qLDPC lends itself to iterative soft decoding quite naturally.…”

Section: A Design and Construction Of Qldpcmentioning

confidence: 99%

An Iteratively Decodable Tensor Product Code with Application to Data Storage

Alhussien¹,

Moon

2010

IEEE J. Select. Areas Commun.

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Abstract-The error pattern correcting code (EPCC) can be constructed to provide a syndrome decoding table targeting the dominant error events of an inter-symbol interference channel at the output of the Viterbi detector. For the size of the syndrome table to be manageable and the list of possible error events to be reasonable in size, the codeword length of EPCC needs to be short enough. However, the rate of such a short length code will be too low for hard drive applications. To accommodate the required large redundancy, it is possible to record only a highly compressed function of the parity bits of EPCC's tensor product with a symbol correcting code. In this paper, we show that the proposed tensor error-pattern correcting code (T-EPCC) is linear time encodable and also devise a low-complexity soft iterative decoding algorithm for EPCC's tensor product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a 1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same decoder complexity.Index Terms-Tensor product codes, inter-symbol interference, turbo equalization, error-pattern correction, q-ary LDPC, multi-level log likelihood ratio, tensor symbol signatures, signature-correcting code, detection postprocessing.

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A class of good quasi-cyclic low-density parity check codes based on progressive edge growth graph

Cited by 79 publications

References 11 publications

Investigation of random-structure regular LDPC codes construction based on progressive edge-growth and algorithms for removal of short cycles

Investigation of random-structure regular LDPC codes construction based on progressive edge-growth and algorithms for removal of short cycles

Channel Coding Toward 6G: Technical Overview and Outlook

An Iteratively Decodable Tensor Product Code with Application to Data Storage

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