Research On Decoding Algorithms Of LDPC Codes

LDPC code has the advantages of closeing to the Shannon limit, the powerful error correction capability, the lower decoding algorithm complexity and being easy to implement, so it has become the research focus of coding. At the same time, the study of its application is unfolded in a wide range.This article mainly aimed at two aspects.These were the high complexity of LLR BP algorithm for decoding and the high performance loss of BP-Based algorithm. The Normalized BP-Based algorithm is multiplied by a correction factor to compensate for the loss of performance of the BP-Based algorithm. This is a linear compensation. In this article the nonlinear compensation was used to further improve the decoding performance after the analysis. So the idea of using variable correction factor on Normalized BP-Based algorithm was occurred. The variable correction factor algorithm based on the mean classification was proposed.In order to reduce the complexity of the mean classification, the variable correction factor algorithm based on the count classification was proposed. In order to reduce the complexity of LLR BP algotithm, researchers once fitted the exponential and logarithmic functions respectively, but this method easily lead to error accumulation. To further improve the fitting results,this article used uneven segments and non-uniform sampling intervals to fit the entire nonlinear function as a whole based on the principle of least squares method.The mainly work in this article is as follows:Firstly, read lots of information to understand the characteristics of LDPC code, the significance of the study and the status quo.Secondly, recursed decoding algorithms based on BP’s in detail and analyzed the algorithms’performance by simulation. And also analyzed the various factors affected the decoding performance of LDPC codes.Thirdly, the variable correction factor algorithm based on the mean classification was proposed by analying the mean and variance of the information passed from variable nodes to check nodes. The BER performance, the number of iterations and the complexity of this algorithm were analyzed.Next compared this algorithm with other decoding algorithms. Simulation result indicates that when the bit error rate is10-3, the improved algorithms can get about0.1dB gain camparing with Normalized BP-Based algorithm and can get about0.3dB gain comparing with LLR BP algorithm, and the number of iterations is not added. However, due to the introduction of the mean calculation, the complexity is increased. To avoid the excessive increase in complexity, limited the degree of check node to less than or equal to6.Fourthly, In order to improve the shortcomings of variable correction factor algorithm based on the mean classification. Variable correction factor algorithm based on the count classification was proposed. Next the BER performance, the number of iterations and the complexity of this algorithm were analyzed. By comparing with other decoding algorithms, simulation result indicates that when the bit error rate is less than10-3, this algorithm can get about0.2dB gain camparing with Normalized BP-Based algorithm and can get about0.3dB gain comparing with LLR BP algorithm. Variable correction factor algorithm based on the count classification not only improves the decoding performance, but also the number of iterations is relatively small. And it only adds a small amount of comparison operators.Fifthly, curve fitting algorithm of the LLR BP based on least squares method is proposed.The original function is divided into21segments. The quadratic function and cubic function were used in curve fitting based on the least square method respectively. The decimal factors of coefficients of each fit function argument retain five decimal and four decimal respectively. The BER performance, the number of iteration and the complexity of the two fit functions were analyzed detailedly. By comparing the performance and the complexity with the cubic fit function, the quadratic fitting function of reserving five decimal is better. When the signal-to-noise ratio is from2dB to3dB, the performance of this algorithm is better than the LLR BP algorithm. And when the bit error rate is about10-3, it can get about0.1dB gain.