Entanglement-Assisted Quantum Quasi-Cyclic Low-Density Parity-Check Codes

Details Entanglement-Assisted Quantum Quasi-Cyclic Low-Density Parity-Check Codes Entanglement-Assisted Quantum Quasi-Cyclic Low-Density Parity-Check Codes

2008-03-02

arxiv.org/abs/0803.0100v2

Phys. Rev. A 79, 032340 (2009)

Physics

Quantum Physics

8 pages, 1 figure. Final version that will show up on PRA. Minor changes in contents and Title

Scientific paper

10.1103/PhysRevA.79.032340

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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