Quasi-cyclic low-density parity-check （QC-LDPC） codes can be constructed conveniently by cyclic lifting of protographs. For the purpose of eliminating short cycles in the Tanner graph to guarantee performance, first an algorithm to enumerate the harmful short cycles in the protograph is designed, and then a greedy algorithm is proposed to assign proper permutation shifts to the circulant permutation submatrices in the parity check matrix after lifting. Compared with the existing deterministic edge swapping （DES） algorithms, the proposed greedy algorithm adds more constraints in the assignment of permutation shifts to improve performance. Simulation results verify that it outperforms DES in reducing short cycles. In addition, it is proved that the parity check matrices of the cyclic lifted QC-LDPC codes can be transformed into block lower triangular ones when the lifting factor is a power of 2. Utilizing this property, the QC- LDPC codes can be encoded by preprocessing the base matrices, which reduces the encoding complexity to a large extent.
Principles and performances of quantum stochastic filters are studied for nonlinear time-domain filtering of communication signals. Filtering is realized by combining neural networks with the nonlinear Schroedinger equation and the time-variant probability density function of signals is estimated by solution of the equation. It is shown that obviously different performances can be achieved by the control of weight coefficients of potential fields. Based on this characteristic, a novel filtering algorithm is proposed, and utilizing this algorithm, the nonlinear waveform distortion of output signals and the denoising capability of the filters can be compromised. This will make the application of quantum stochastic filters be greatly extended, such as in applying the filters to the processing of communication signals. The predominant performance of quantum stochastic filters is shown by simulation results.
