Spatially coupled quasi-cyclic quantum LDPC codes

• Published in: 2011 IEEE International Symposium on Information Theory Proceedings pp. 638 - 642
• Main Authors: Hagiwara, M., Kasai, K., Imai, H., Sakaniwa, K.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.07.2011
• Subjects: Cascading style sheets; Convolutional codes; CSS codes; Decoding; Error correction codes; High definition video; Iterative decoding; LDPC code; Parity check codes; Quantum error-correcting codes; Sparse matrices; Spatial coupling
• ISBN: 1457705966; 9781457705960
• ISSN: 2157-8095; 2157-8117
• DOI: 10.1109/ISIT.2011.6034208

For designing low-density parity-check (LDPC) codes for quantum error-correction, we desire to satisfy the conflicting requirements below simultaneously. 1) The row weights of parity-check "should be large": The minimum distances are bounded above by the minimum row weights of parity-check matrices of constituent classical codes. Small minimum distance tends to result in poor decoding performance at the error-floor region. 2) The row weights of parity-check matrices "should not be large": The performance of the sum-product decoding algorithm at the water-fall region is degraded as the row weight increases. Recently, Kudekar et al. showed spatially-coupled (SC) LDPC codes exhibit capacity-achieving performance for classical channels. SC LDPC codes have both large row weight and capacity-achieving error-floor and water-fall performance. In this paper, we propose a new class of quantum LDPC codes based on spatially coupled quasi-cyclic LDPC codes. The performance outperforms that of quantum "non-coupled" quasi-cyclic LDPC codes.