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Finite field construction for quasi-cyclic LDPC convolutional codes with cyclic 2-D MDS codes

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Abstract

The parity-check matrices for quasi-cyclic low-density parity-check convolutional (QC-LDPC-C) codes have different characteristics of time-varying periodicity and need to realize fast encoding. The finite field construction method for QC-LDPC-C codes with cyclic two-dimensional maximum distance separable (2-D MDS) codes is proposed using the base matrix framework and matrix unwrapping, thus the constructed parity-check matrices are free of length-4 cycles. The unwrapped matrices are constructed respectively based on different cyclic 2-D MDS codes for the case of matrix period less than or greater than constraint block length, and construction examples are given. LDPC-C codes with different periodicity characteristics are compared with QC-LDPC-C codes constructed with the proposed method. Experimental results show that QC-LDPC-C codes with the proposed method outperform the other codes and have lower encoding and decoding complexity.

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Funding

This work was supported by the National Natural Science Foundation of China under Grant number 61771047 and the application of China national terrestrial digital TV system research (The Next Generation) project.

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Authors and Affiliations

  1. China Academy of Electronic and Information Technology (CAEIT), China Electronic Technology Group Corporation (CETC), Beijing, 100041, China

    Ming Zhao & Zhipeng Liu

  2. School of Electronics and Information Engineering, Beihang University, Beijing, 100191, China

    Ling Zhao

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  1. Ming Zhao
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  2. Zhipeng Liu
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Correspondence to Ming Zhao.

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Zhao, M., Liu, Z. & Zhao, L. Finite field construction for quasi-cyclic LDPC convolutional codes with cyclic 2-D MDS codes. Telecommun Syst 81, 115–123 (2022). https://doi.org/10.1007/s11235-022-00926-x

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