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IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

Explicit Construction of QC-LDPC Codes Without Short Cycles via Shifting Dual Increasing Sequences

Guohua Zhang, Mei Li, Yi Fang

Published Sep 1, 2026• 0 citations
Publisher
DOI
10.1109/pimrc69400.2026.11711944

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Low-density Parity-check (LDPC) coding is a class of advanced channel coding techniques. To improve the performance of LDPC codes, a simple and effective method to construct QC-LDPC codes without short cycles (cycles of length four and six) is proposed. The approach is especially effective when the parity-check matrix of QC-LDPC codes is composed of circulant permutation matrices. Firstly, we analyze the shapes of the cycles in the exponent matrix, to get the required conditions of no four-cycles and six-cycles. Then we show how to construct the parity-check matrix without four-cycles and six-cycles by filling rows of the exponent matrix with arithmetic sequences. Simulation results show that the proposed codes have better performance than array codes. Though the performance of the proposed codes is not as well as random codes at higher Eb/N0, they can be applied to practical communications because of being encoded in linear time with shift registers.
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes have practical significance in the field of engineering, thus their construction algorithm is a hot issue in the field of LDPC codes. Based on existing construction methods, particularly the method based on Progressive Edge-Growth (PEG) algorithm, a new construction method of shift matrix is proposed. It can effectively avoid the copy of cycle structures, especially short cycles in base matrix after extension. Besides, it also relieves the time cost caused by random search, and greatly improves the length of cycles when compared with algorithms based on methods such as quadratic congruence and arithmetic sequence. Those algorithms can only eliminate short cycles with length 4, while our method can provide QC-LDPC codes without length 6 at least. Cycle analysis and simulation results show that the newly constructed QC-LDPC codes have good cycle structure and error correction performance.
By utilizing a Sidon sequence, two new methods are proposed to construct quasi-cyclic (QC) low-density parity-check (LDPC) codes. The first method yields a QC-LDPC code without 4-cycles and the second method gives a QC-LDPC code without 4-cycles and 6-cycles. In the literature there are two methods which employ mathematical objects somewhat resembling a Sidon sequence to remove 4-cycles, and there are two explicit constructions which guarantee the absence of 4-cycles and 6-cycles. Compared with the former, our first method is much more flexible in selecting parameters while providing identical or better performance. Compared with the latter, our second method provides much better performance.