Short Girth-8 QC-LDPC Codes Constructed from Vertically Symmetric Exponent Matrices

核心概念

A novel construction framework based on vertical symmetry (VS) is proposed to efficiently generate short girth-8 quasi-cyclic low-density parity-check (QC-LDPC) codes.

摘要

The paper presents a new structure called vertical symmetry (VS) for the exponent matrices of QC-LDPC codes. It aims to address the challenge of constructing short girth-8 QC-LDPC codes.
The key highlights are:

Basic properties of the VS structure are introduced, which enable the transformation of existing explicit constructions into the VS form.

Two novel explicit constructions with the VS structure are proposed for column weights of three and six, guaranteeing short codes.

An efficient search-based method is also developed to find short codes with the VS structure.

Compared to state-of-the-art benchmarks, both the explicit constructions and the search-based method can provide shorter codes for most cases. Simulation results show that the new shorter codes can perform almost the same as or better than the longer existing counterparts, making them suitable for low-latency communication systems.

統計資料

To address the challenge of constructing short girth-8 quasi-cyclic (QC) low-density parity-check (LDPC) codes, a novel construction framework based on vertical symmetry (VS) is proposed.
The proposed VS-based QC-LDPC codes have shorter lengths for most row weights compared to the state-of-the-art benchmarks.

引述

"A novel construction framework based on vertical symmetry (VS) is proposed to efficiently generate short girth-8 quasi-cyclic low-density parity-check (QC-LDPC) codes."
"Compared to state-of-the-art benchmarks, both the explicit constructions and the search-based method can provide shorter codes for most cases."

從以下內容提煉的關鍵洞見

Short Regular Girth-8 QC-LDPC Codes From Exponent Matrices with Vertical Symmetry

by Guohua Zhang... 於 arxiv.org 04-24-2024

https://arxiv.org/pdf/2404.14962.pdf

深入探究

How can the proposed VS structure be extended to construct short girth-10 or girth-12 QC-LDPC codes?

The proposed Vertical Symmetry (VS) structure can be extended to construct short girth-10 or girth-12 QC-LDPC codes by modifying the construction framework based on the properties of the VS structure.
For girth-10 codes, the VS structure can be adapted by considering the constraints and properties required to ensure a minimum girth of 10 in the LDPC codes. By adjusting the relationships between the elements in the exponent matrices and the circulant sizes, it is possible to construct QC-LDPC codes with a girth of 10 while maintaining short lengths. This extension would involve exploring new explicit constructions and search-based methods that adhere to the girth-10 requirements.
Similarly, for girth-12 codes, the VS structure can be further developed to accommodate the constraints necessary for achieving a girth of 12 in the LDPC codes. By analyzing the relationships between the elements in the exponent matrices and introducing suitable transformations, it is feasible to design QC-LDPC codes with a girth of 12 and shorter lengths. This extension would involve refining the construction techniques and algorithms to meet the specific criteria for girth-12 codes.
In essence, extending the proposed VS structure to construct short girth-10 or girth-12 QC-LDPC codes would involve customizing the construction methods to satisfy the requirements for higher girth values while maintaining the compactness and efficiency of the codes.

What are the potential applications of the shorter QC-LDPC codes beyond low-latency communication systems?

The shorter QC-LDPC codes derived from the proposed VS structure have various potential applications beyond low-latency communication systems. Some of the key applications include:

Satellite Communications: Shorter QC-LDPC codes can be beneficial in satellite communications systems where bandwidth and power efficiency are crucial. The compact nature of these codes allows for efficient data transmission over satellite links, improving overall system performance.

Wireless Networks: In wireless networks, shorter QC-LDPC codes can enhance the reliability and throughput of data transmission. These codes can be utilized in 5G and upcoming 6G networks to support high-speed communication with reduced latency.

Storage Systems: Short girth QC-LDPC codes are valuable in storage systems for error correction and data protection. By implementing shorter codes, storage devices can achieve higher data integrity and reliability, leading to improved storage efficiency.

IoT Devices: Internet of Things (IoT) devices often operate under resource-constrained environments. Shorter QC-LDPC codes can be applied in IoT devices to optimize data transmission, reduce energy consumption, and enhance connectivity reliability.

Digital Broadcasting: In digital broadcasting systems, shorter QC-LDPC codes can improve the robustness of signal transmission, leading to better reception quality and error correction capabilities.

Overall, the shorter QC-LDPC codes can find applications in various domains where efficient and reliable data transmission is essential, contributing to enhanced performance and connectivity in diverse communication systems.

Can the ideas behind the VS structure be applied to other coding schemes beyond QC-LDPC codes to achieve shorter lengths?

The concepts and principles underlying the Vertical Symmetry (VS) structure can be adapted and applied to other coding schemes beyond QC-LDPC codes to achieve shorter lengths. By leveraging the symmetry properties and construction techniques inherent in the VS structure, similar benefits can be realized in different coding schemes. Here are some ways the ideas behind the VS structure can be extended to achieve shorter lengths in other coding schemes:

LDPC Convolutional Codes: The VS structure principles can be utilized to design shorter LDPC convolutional codes by incorporating symmetry properties and optimized construction methods. This can lead to more compact and efficient codes for use in various communication systems.

Turbo Codes: The concepts of symmetry and structured construction from the VS structure can be applied to Turbo codes to develop shorter and more effective coding schemes. By exploring symmetry in interleavers and component codes, shorter Turbo codes with improved performance can be designed.

Polar Codes: The VS structure ideas can be adapted to Polar codes to create shorter code lengths while maintaining error correction capabilities. By introducing symmetry and structured transformations, Polar codes can be optimized for reduced lengths and enhanced efficiency.

Reed-Solomon Codes: Applying the principles of the VS structure to Reed-Solomon codes can result in shorter block lengths with robust error correction capabilities. By incorporating symmetry properties and tailored encoding techniques, Reed-Solomon codes can be optimized for various applications.

In conclusion, the ideas behind the VS structure can be extended and applied to a wide range of coding schemes beyond QC-LDPC codes to achieve shorter lengths and improved performance in diverse communication and data storage systems.