Quantum quasi-cyclic low-density parity-check codes

Ivan B. Djordjević

河本大輝, Daiki Komoto, Kenta Kasai

Explicit Construction of Quantum Quasi-Cyclic Low-Density Parity-Check Codes with Column Weight 2 and Girth 12, Explicit Construction of Quantum Quasi-Cyclic Low-Density Parity-Check Codes with Column Weight 2 and Girth 12

Shu Lin, Lei Chen, Jun Xu +1 more

The paper presents two classes of quasi-cyclic low-density parity-check (LDPC) codes which perform close to the Shannon limit. The construction of these codes is based on decomposition of circulant matrices constructed from finite geometries.

Ivan B. Djordjević

Gianluigi Liva, W.E. Ryan, Marco Chiani

In this paper, a novel methodology for designing structured generalized low-density parity-check (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call low-density parity-check (LDPC) code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.

Fanny Terrier