Entanglement-assisted quantum quasicyclic low-density parity-check

American Physical Society
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Journal article
Hsieh, Min-Hsiu, Brun, Todd, and Devetak, Igor 2009, 'Entanglement-assisted quantum quasicyclic low-density parity-check', Physical Review A, vol. 79, no. 3, pp. 032340-1-032340-8.
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We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasi-cyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Shor-Steane (CSS) construction do not need to satisfy the dual-containing property as long as pre-shared entanglement is available to both sender and receiver. We can use this to avoid the many 4-cycles which typically arise in dual-containing LDPC codes. The advantage of such quantum codes comes from the use of efficient decoding algorithms such as sum-product algorithm (SPA). It is well known that in the SPA, cycles of length 4 make successive decoding iterations highly correlated and hence limit the decoding performance. We show the principle of constructing quantum QC-LDPC codes which require only small amounts of initial shared entanglement.
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