Abstract
The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Experimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.
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Supported by the National Natural Science Foundation of China (No. 61071145, 41074090), and the Specialized Research Fund for the Doctoral Program of Higher Education (200802880014).
Communication author: Cao Dong, born in 1974, male, Ph.D.. candidate.
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Cao, D., Song, Y. & Zhao, S. A novel construction of quantum ldpc codes based on cyclic classes of lines in euclidean geometries. J. Electron.(China) 29, 1–8 (2012). https://doi.org/10.1007/s11767-012-0817-8
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DOI: https://doi.org/10.1007/s11767-012-0817-8
Key words
- Quantum Error-Correcting Codes (QECC)
- Low Density Parity Check (LDPC) codes
- Finite geometry
- Euclidean Geometry (EG)
- Stabilizer codes
- Quasi-cyclic codes