Spatially Coupled Quasi-Cyclic Quantum LDPC Codes

学 萩原, Manabu Hagiwara, Kenta Kasai +3 more

Manabu Hagiwara, Kenta Kasai, Hideki Imai +1 more

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.

Kenta Kasai, Kenta Kasai

Keke Liu, Mostafa El‐Khamy, Jungwon Lee +2 more

This paper considers the algebraic construction and performance of non-binary spatially-coupled low density parity check (LDPC) codes. A replicate-and-mask approach is presented to construct finite-length algebraic quasi-cyclic (QC) spatially-coupled (SC) LDPC codes. Numerical results show the superiority of non-binary algebraic SC QC LDPC codes over the corresponding random non-binary (block and SC) LDPC codes. In this paper, it is demonstrated that the threshold saturation phenomenon, previously demonstrated for binary SC LDPC codes, also holds for non-binary SC LDPC codes over the binary-input AWGN channel with BPSK modulation.

Kenta Kasai

Xueqin Jiang, Siyuan Yang, Peng Huang +1 more

The speed of continuous variable quantum key distribution is limited by the reconciliation efficiency and the reconciliation frame error rate (FER) in the reconciliation phase. In this paper, we propose an approach that may increase the reconciliation efficiency and decrease the FER. In detail, to increase the reconciliation efficiency, rather than using the block low-density parity-check (LDPC) codes, such as quasi-cyclic LDPC codes, multiedge-type LDPC codes, and punctured LDPC codes, this paper introduces spatially coupled (SC) LDPC codes to the reconciliation phase. To decrease the FER, we propose a new reconciliation scheme based on the special structure of SC-LDPC codes. To demonstrate the performance of the proposed approach, we construct the SC-LDPC codes based on quasi-cyclic repeat-accumulate codes. It is shown that the proposed scheme leads to higher reconciliation speed than that of the previous reconciliation schemes.