Low Density Parity Check (LDPC) Forward Error Correction ...
Error Correction using Quantum Quasi-Cyclic Low Density Parity Check (LDPC)Codes
Transcript of Error Correction using Quantum Quasi-Cyclic Low Density Parity Check (LDPC)Codes
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Error Correction using Quantum Quasi-Cyclic
Low Density Parity Check (LDPC) Codes
Lin Jing
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Why use LDPC code
Classical LDPC code can approach Shannon Capacity Efficient decoders
Main Obstacle is dual containing constraint.
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CSS Construction
Use C as parity check matrix for X error, and the dual code of C as parity check matrix for Z error
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“Quantum Quasi-Cyclic LDPC Codes”, Manabu et. al, IEEE Intl. Symp. Inform. Theory, 2007
Generate Parity Check Matrices
A computational method:
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Use this method, we can generate Hc and HD
They are dual code of each other.
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1 10 27 51 72 63 46 22 29 71 53 19 44 2 20 5422 1 10 27 51 72 63 46 71 53 19 44 2 20 54 2946 22 1 10 27 51 72 63 53 19 44 2 20 54 29 7163 46 22 1 10 27 51 72 19 44 2 20 54 29 71 5372 63 46 22 1 10 27 51 44 2 20 54 29 71 53 1951 72 63 46 22 1 10 27 2 20 54 29 71 53 19 4427 51 72 63 46 22 1 10 20 54 29 71 53 19 44 210 27 51 72 63 46 22 1 54 29 71 53 19 44 2 20
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44 2 20 54 29 71 53 19 72 63 46 22 1 10 27 5119 44 2 20 54 29 71 53 63 46 22 1 10 27 51 7253 19 44 2 20 54 29 71 46 22 1 10 27 51 72 6371 53 19 44 2 20 54 29 22 1 10 27 51 72 63 4629 71 53 19 44 2 20 54 1 10 27 51 72 63 46 2254 29 71 53 19 44 2 20 10 27 51 72 63 46 22 120 54 29 71 53 19 44 2 27 51 72 63 46 22 1 10 2 20 54 29 71 53 19 44 51 72 63 46 22 1 10 27
Rows: 584 Columns: 1168
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Deleted rows: 146/584Code rate: 25%
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Sum-Product Alg. Decoder
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Use different error probability setting for decoder
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