Design of High-Rate LDPC Codes Based on Matroid Theory

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.

Authors:
Wu Guangfu, Lv Yijie, He Jiguang

Publication type:
A1 Journal article – refereed

Place of publication:

Keywords:
bit error rate, Girth condition, high rate, matroid theory, parity-check matrix

Published:

Full citation:
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

DOI:
https://doi.org/10.1109/LCOMM.2019.2940977

Read the publication here:
http://urn.fi/urn:nbn:fi-fe202001303926