333 research outputs found
Entanglement-Assisted Quantum Quasi-Cyclic Low-Density Parity-Check Codes
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.Comment: 8 pages, 1 figure. Final version that will show up on PRA. Minor
changes in contents and Titl
- …