G. Wu, Y. Lv and J. He, "Design of High-Rate LDPC Codes Based on Matroid Theory," in IEEE Communications Letters, vol. 23, no. 12, pp. 2146-2149, Dec. 2019. doi: 10.1109/LCOMM.2019.2940977

### Design of high-rate LDPC codes based on matroid theory

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Author: Wu, Guangfu1; Lv, Yijie1; He, Jiguang2
Organizations: 1Dept. of Information Engineering, Jiangxi University of Science and Technology, Jiangxi, China
2Centre for Wireless Communications, University of Oulu, FI-90014, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
Language: English
Published: Institute of Electrical and Electronics Engineers, 2019
Publish Date: 2020-01-30
Description:

# Abstract

In this letter, sufficient conditions for the determination of the girth are studied from the perspective of matroid theory. The girth of a Tanner graph is at least $2(t_{1}+2)$ if $t_{1}$ specific conditions are simultaneously met. A novel method of constructing high-rate low-density parity-check (LDPC) codes is proposed based on the matroid theory. The parity-check matrices of the constructed LDPC codes are in the form of H = [I $\vert$ H 2 ] with H 2 constructed under the conditions of a given girth and a fixed column weight (e.g., $W_{c}=4$ or $W_{c}=6$ ). Simulation results verify that the proposed LDPC codes outperform those in the literature over additive white Gaussian noise channels in terms of bit error rate performance.

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Series: IEEE communications letters
ISSN: 1089-7798
ISSN-E: 2373-7891
ISSN-L: 1089-7798
Volume: 23
Issue: 12
Pages: 2146 - 2149
DOI: 10.1109/LCOMM.2019.2940977