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Journal of Nanjing University of Posts and Telecommunications

A Coset Searching Algorithm Based on Quantum Low-density-parity-check Codes

Yue Ke-feng

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Based on the classical LDPC construction method and quantum error correction techniques,a construction method of quantum low-density-parity-check codes is discussed and a novel coset searching algorithm which is important in the construction method is developed in this paper.We select quantum code(3,8)(16,6) as an example to verify this algorithm and compare it with the conventional one.The result shows that the algorithm can improve the encoding efficiency and reduce complexity with the same performance as the conventional one.At the same time,the algorithm can slove the problem of storage of quantum codes.

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Electronics Letters•Oct 1, 2014•5 citations
Based on the classical LDPC construction method and quantum error correction techniques,a construction method of quantum low-density-parity-check codes is discussed and a novel coset searching algorithm which is important in the construction method is developed in this paper.We select quantum code(3,8)(16,6) as an example to verify this algorithm and compare it with the conventional one.The result shows that the algorithm can improve the encoding efficiency and reduce complexity with the same performance as the conventional one.At the same time,the algorithm can slove the problem of storage of quantum codes.
With the development of quantum error correction techniques, many counterparts of classical error correction coding techniques have been found in quantum area. As the quantum counterpart of a good error correction code in classical communications, quantum low density parity check code becomes a promising coding technique in quantum error correction area. In this paper, a construction method of quantum low density parity check code (quantum LDPC) based on Projective Geometry is proposed, and the quantum code QLDPC [21,6] is selected as an example to illustrate the whole construction procedures. By numerical simulation, the error correction performance of QLDPC [21,6] is discussed over the bit-flipping channel. It is shown that this method is available and has some advantages.
Quantum error correction is the basic technique for realization of quantum communication and quantum computation.So far,the theories of quantum error correction has become more and more perfect,many counterpart of classical error correction coding technique have been found in quantum area.In this paper,we improve a method of construction of parity check matrix in quantum low density parity check(LDPC) codes based on sparse circle sequence,and compare the performance of our construction method with that of MacKay's.The result shows that our method is not only able to remove some disadvantages of B and U construction,but also to reserve their advantages and improve the efficiency of coding and decoding.
In this paper, a construction method of quantum low density parity check codes (quantum LDPC) which based on classical quasi-cyclic sparse sequence is proposed, and the quantum code QLDPC(3,8)(16,6) and QLDPC(3,8)(64,24) are selected as examples to illustrate this construction method. The performances of this kind quantum LDPC codes are discussed over the bit-flipping channel by numerical simulations. The results show that these quantum codes have good ability to correct error in quantum channel.
Quantum error correction is the basic technique for realization of quantum communication and quantum computation. So far, the theories of quantum error correction have become more and more perfect, and many counterpart of classical error correction coding technique have been found in quantum area. In this article, we proposed a new method of construction of parity check matrix of quantum low density parity check (LDPC) codes which based on classical quasi-cyclic LDPC codes, and selected the quantum code (3,8)(16,6) as the example to illustrate the construction of quantum code. We also gave its completing circuit by controlled-not gate and Hadamard gate.
A simple and efficient search method based on the coset concept is proposed to construct (3, L ) quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes without small cycles. Compared with the random search method, the chance to find large‐girth codes is remarkably increased for the new method. Compared with Tanner's construction, the proposed method is much more flexible in the selection of row weight L . Some new codes are constructed with the shortest lengths compared with those constructed by the existing well‐known methods. Simulation results show that the novel codes with moderate length perform well in the additive white Gaussian noise channel.