Research On The Decoding Of Quantum Spatially Coupled LDPC Codes

In recent years,with the continuous progress of quantum technology,people have increasingly realized that it is difficult to achieve practical application of quantum information technology without solving the problem of noise interference.Like classical information processing,quantum error correction codes are also the key means for quantum information systems to overcome noise.In the design of quantum error correction codes,the decoding research of quantum codes has been paid more and more attention.In the classical domain,spatially coupled LDPC codes(SC-LDPC)are,due to their properties that the belief propagation(BP)decoding threshold is close to the maximum a posteriori probability(MAP)decoding threshold and that the parity check matrix has a nonzero diagonal band structure,received extensive attention.Especially its sliding window decoding algorithm and subsequent improved algorithms have improved the decoding performance and decoding delay of SC-LDPC codes,and further expanded its application field.However,in the research of quantum error correction codes,the decoding research of quantum SC-LDPC codes has not made much progress.Based on the structural characteristics of quantum SC-LDPC codes and the idea of sliding window decoding in classical theory,this paper analyzes the decoding of quantum SC-LDPC codes systematically,and a quantum double-window sliding decoding scheme is proposed.According to the classical idea of suppressing errors generated during the window sliding decoding process,the optimized algorithm of the quantum double-window simultaneous backtracking and expanding window is given.The specific work is as follows:1.A quantum double-window sliding decoding algorithm suitable for quantum SC-LDPC codes is proposed.In this paper,according to the structural characteristics of quantum SCLDPC and the idea of sliding window decoding algorithm in classical theory,a quantum double-window sliding decoding scheme is proposed.The simulation verification of the quantum double-window sliding decoding scheme is presented.2.On the basis of the above quantum SC-LDPC code decoding scheme,an optimization algorithm for simultaneous backtracking expansion of quantum double windows is proposed.In this paper,through the study of classic SC-LDPC codes,combined with its idea of suppressing error propagation in the sliding window decoding process,combined with the strategy of backtracking and expanding the window to suppress errors.An optimization algorithm for simultaneous backtracking expansion of quantum double windows is proposed,and the algorithm is verified by simulation analysis.3.Aiming at the optimization algorithm of simultaneous retrospective expansion of quantum double windows proposed in this paper,the size of the expanded window is explained according to the check gradient relationship between variable nodes,and the method is analyzed from the comprehensive point of view of complexity and performance.