The Research Of Decoding Algorithms For LDPC Codes Based On Density Evolution

LDPC(Low-Density Parity-Check)codes are the block error-correction codes with the sparse check matrix,and their performance are close to Shannon limit.Because of their superior performance,LDPC codes have been widely used in the communication standards,such as WiMax(Worldwide Interoperability for Microwave Access)and DTMB(Digital Television Terrestrial Multimedia)standards.What's more,in the 5G communication standard,LDPC codes have been established as the coding scheme in data channel,which makes LDPC codes have been great academic interest recently.GA(Gaussian Approximation)is a simplified analysis method compared with DE(Density Evolution)theory,so it is significant to research GA.In this paper,we present GA of the TDMP(Turbo Decoding Message Passing)algorithm based on GA of the BP(Belief Propagation)algorithm.When using GA to analyze the decoding convergence of the TDMP algorithm,we can provide theoretical basis for proving the superiority of the TDMP algorithm.We simulate the BP algorithm and the TDMP algorithm under WiMax standard.The simulation results show that the decoding convergence speed of the TDMP algorithm is faster and the number of iterations is fewer compared with the BP algorithm under the same conditions.Using GA instead of DE,the simple one-dimensional average evolution can replace the complicated high dimensional DE,thus,which can make it more convenient to analysis and optimize LDPC codes,and at the same time to calculate the threshold of channel parameters.In the paper,under WiMax standard,the thresholds of the TDMP algorithm based on DE and GA are provided,respectively.The gaps of them are only0.03 ~ 0.08 dB.In this paper,we combine the BP algorithm and its simplified algorithms to present an improved min sum algorithm called the DE Min Sum algorithm based on DE for LDPC codes.First,we use DE theory to calculate the PMF(Probability Mass Function)of the messages that are send form the check nodes to variable nodes of the BP algorithm and the MS(Min Sum)/NMS(Normalized Min Sum)algorithm,andfurthermore to calculate the normalized factor ?.Then,the ? is modified further by using weighted average.Finally,in order to ensure the decoding performance and reduce the hardware complexity,the same ? is used for different SNR(Signal to Noise Ratio).The simulation results show that a gain of about 0.2 dB can be achieved in comparison with the classical NMS algorithm.In addition,this improved algorithm can obtain the same decoding performance compared with the LMMSE(Linear Minimum Mean Square Error)Min Sum algorithm whose decoding performance is very close to that of the BP algorithm,and it can also save around24.57% of logic elements and 34.33% of memory bits compared with the LMMSE Min Sum algorithm at the same time.