A Performance Analysis of Quantum Low-Density Parity-Check Codes for Correcting Correlated Errors
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A Performance Analysis of Quantum Low-Density Parity-Check Codes for Correcting Correlated Errors Jihao Fan1,2 Received: 5 June 2020 / Accepted: 10 October 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper we analyse the performance of quantum low-density parity-check (LDPC) codes over quantum memory channels for correcting correlated errors, where the quantum LDPC codes we use are the hypergraph product quantum LDPC codes. We generalize the classical Gilbert-Elliot markovian memory channel to the quantum Gilbert-Elliot channel and use it to model the memory effect in quantum memory channels. The simulation results show the memory effects in quantum GE channels has a bad effect to the performance of hypergraph product quantum LDPC codes. Then we propose a concatenation scheme by serially concatenating two hypergraph product quantum LDPC codes and it is shown that the serial concatenation scheme can improve the performance of hypergraph product quantum LDPC codes and lower down the error floor over quantum GE channels. Keywords Low-density parity-check code · Quantum memory channel · Gilbert-Elliot channel · Hypergraph product · Quantum error correction code.
1 Introduction In quantum communication systems, quantum noise can be spatially and timely independent or correlated with each other. And in the practical communication systems, errors usually appear in some continuous positions rather than in random, e.g., the burst of errors. In classical communications, the Gilbert-Elliot (GE) channel [1, 2] is a useful Markovian model to characterize the memory phenomenon in the practical communication channels. In such channel model, the channel is assumed to either be in a good state with a relative small error probability, or in a bad state with a much larger error probability. And there is a probability that the channel may transform from a good state to a bad one, or vice verse. In quantum
Jihao Fan
[email protected] 1
School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu Province, China
2
Key Laboratory of Computer Network and Information Integration of Ministry of Education, Southeast University, Nanjing, 211189, China
International Journal of Theoretical Physics
memory channels, the memory effect also leads to correlated or burst of errors [3–5]. If the correlated error is a long burst, in [6–9], it is shown that quantum burst error correction codes (QBECCs) are effective to correct long burst of errors and QBECCs are usually more efficient than standard random quantum codes. However, the long burst of errors only happens in some special memory channels [10] and it is shown that the performance of single burst error correction code is not ideal in classical GE channel [11, 12]. Classical LDPC codes are a class of sparse graph codes which have excellent error correction performance with an efficient iterative decoding algorithm [13]. LDPC codes can be decoded by using the belief-propagation
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