Research On Construction Methods Of Low-density Parity-check Codes

Low-Density Parity-Check(LDPC) codes are becoming a hot-topic in recent years because of their relatively simple iterative decoding structure and near Shannon limit performance.Based on the research subject of National nature and science foundation——the foundation project of efficient encoding in new generation of air-management,we study the decoding methods,the classic analysis and construction methods of LDPC codes,especially the design of degree distributions and construction of check matrix.The main work and innovations of this thesis are as follows:1.Based on the research of decoding algorithm and density evolution theory of LDPC codes,we calculate the decoding threshold of many regular LDPC codes with 0.5 code-rates using density evolution and different decoding methods.After the research of classic construction methods of LDPC codes,we use MacKay's methods construct(4000,3,6),(8000,3,6) codes,use finite geometry methods construct EG(1023,781) codes,and then,simulate their performance under sum product decoding algorithm.2.By reform the evolution methods and stop criterion of differential evolution algorithm, we design some good degree distributions with 0.5 code-rates under binary eraser channel and additive white Gaussian noisy channel using density evolution.The simulation results present that the reformed algorithm can converge faster.Using Gaussian approximation,we find the degree distributions that we designed possess bigger decoding thresholds.3.We present a new method to construct check matrix.In this method,we use the natrix that constructs by random construction based on degree distributions as base-matrix.And then we replace the elements of the base-matrix using the circulated identity matrix and all zero-matrix to expand the base-matrix.We prove that even the base-matrix has 4-circle,the minimum circle in the matrix that we construct has length six at least.When the base-matrix possesses the lower triangular form,we prove the matrix we construct can get the lower triangular form as the same way.Since,it has efficient encoding methods.The method we present has low complication in matrix construction and efficient encoding management.