The Improved Degree Distribution Design Of LT Code

People's communication quality requirements are getting higher and higher with the continuous development of wireless communications technology in today's society.However,the wireless channel to be susceptible of noise interference makes errors in the transmission of information.The reliability of information transmission is an important part of modern communication technology.Now fountain code has been everyone's attention because it is an error correction code of overhead of decoding to have less redundancy and coding simple.However,due to the degree distribution design,that the traditional fountain code has the disadvantage which the length of the short code overhead of decoding is large.To solve this problem,in this dissertation,the LT code is taken as the research object,and its distribution of Robust Soliton distribution(RSD)is optimized to further reduce the decoding cost and decoding complexity of short code length LT codes.Degree distribution function is the main factor to affect the decoding cost of fountain code.In the design of the traditional LT code,algorithm obtains the ISD degree distribution according to the MP decoding method at the first,but the probability of degree 1 easily disappears in the decoding process to increase the decoding overhead.Therefore,algorithm adds the robustness factor to increase probability distribution of increasing 1 and other low degrees to get the distribution of RSD degree.The probability distribution of degree 1 becomes the key to influence the decoding cost.In order to further reduce the decoding overhead of short code length fountain codes,this dissertation presents a new degree distribution design method.According to the influence of the original symbol length of source and the probability distribution of degree 1 on decoding performance,a new degree distribution function with low decoding overhead is proposed.In this dissertation,algorithm chooses the RSD distribution function to take LT coding which based on the code length of k,and proposes that the decoding cost of LT code should be minimized by gradually adjusting the probability of low degree by stepwise searching.First,we get the best enhancement coefficient of degree 1,and then correct the RSD to get a new degree distribution function.The size of degree 2 is adjusted based on the new degree distribution function.The decoding cost is minimized again,and the best enhancement coefficient of degree 2 is obtained,and so on until the optimal decoding cost is found.Since different k will result in different optimal enhancement coefficients.If each code length adopts the search rule,the complexity is higher.Therefore,in this dissertation,some k values are selected to search for the corresponding optimal enhancement coefficient.The mathematical expression about k is fitted by the least square method.Algorithm gets the enhancement coefficient expression about the degree 1 and degree 2 correction,and modifies the traditional RSD to get the RRSD degree distribution function.Only a small amount of k is selected for searching,the expression of the enhancement coefficient can be obtained.Therefore,this dissertation proposes that the least square method can be used to fit the optimal enhancement coefficient with respect to k,which can greatly reduce the searching complexity of the optimal enhancement coefficient.At the same time,the experimental simulation results show that the RRSD distribution obtained in this dissertation can effectively reduce the fountain code decoding overhead compared with the traditional RSD especially in the short code length effect.Dissertation improves the decoding stability and reduce the decoding complexity.