Matlab r2015a qpskmod
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We introduce an ansatz for quantum codes which gives the hypergraph-product (generalized toric) codes by Tillich and Zémor and generalized bicycle codes by MacKay as limiting cases. Quantum Kronecker sum-product low-density parity-check codes with finite rate Error Correction using Quantum Quasi-Cyclic Low-Density Parity-Check(LDPC) Codes. This makes these codes promising as storage blocks in fault-tolerant quantum computation.
MATLAB R2015A QPSKMOD CODE
Our results show that this code family can perform reasonably well even at high code rates, thus considerably reducing the overhead compared to concatenated and surface codes. From the rates of uncorrectable errors under different error weights we can extrapolate the BER to any small error probability. We simulated this system for depolarizing noise on USC's High Performance Computing Cluster, and obtained the block error rate (BER) as a function of the error weight and code rate. The submatrix of Hc is used to correct Pauli X errors, and the submatrix of Hd to correct Pauli Z errors. Using submatrices obtained from Hc and Hd by deleting rows, we can alter the code rate.
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Two distinct, orthogonal matrices Hc and Hd are used.
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Manabu Hagiwara et al., 2007 presented a method to calculate parity check matrices with high girth. Quasi-cyclic LDPC codes can approach the Shannon capacity and have efficient decoders. Jing, Lin Brun, Todd Quantum Research Team We show the principle of constructing quantum QC-LDPC codes which require only small amounts of initial shared entanglement.Įrror Correction using Quantum Quasi-Cyclic Low-Density Parity-Check(LDPC) Codes It is well known that in the SPA, cycles of length 4 make successive decoding iterations highly correlated and hence limit the decoding performance. The advantage of such quantum codes comes from the use of efficient decoding algorithms such as sum-product algorithm (SPA). We can use this to avoid the many four cycles which typically arise in dual-containing LDPC codes. We have shown that the classical codes in the generalized Calderbank-Skor-Steane construction do not need to satisfy the dual-containing property as long as preshared entanglement is available to both sender and receiver. We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasicyclic (QC) LDPC codes with girth greater than or equal to 6. In addition, I show that EA quantum LDPC codes from balanced incomplete block designs of unitary index require only one entanglement qubit to be shared between source and destination.Įntanglement-assisted quantum quasicyclic low-density parity-check codes I show that two basic gates needed for EA quantum error correction, namely, controlled-NOT (CNOT) and Hadamard gates can be implemented based on Mach-Zehnder interferometer. I propose encoder and decoder architectures for entanglement-assisted (EA) quantum low-density parity-check (LDPC) codes suitable for all-optical implementation. Photonic entanglement-assisted quantum low-density parity-check encoders and decoders.