摘要
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. Ex-perimental 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.
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. Ex- perimental 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.
基金
Supported by the National Natural Science Foundation ofChina (No. 61071145,41074090)
the Specialized Research Fund for the Doctoral Program of Higher Education (200802880014)
