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.

Wu Guangfu, Lv Yijie, He Jiguang

Publication type:
A1 Journal article – refereed

Place of publication:

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


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


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