Research On The Performance And Application Of The Spinal Codes

This thesis discusses a new CM(Code Modulation)method,i.e.spinal code,which is also a kind of rateless code.Basically,spinal code is characterized by its usage of hash function and the random,non-linear mapping between information bits and modulation symbols.Spinal code benefits from the performance of CM technology,rateless code and hash function,and exihibits good throughput performance.It provides a new way to design modern coding and modulation.This thesis focuses on studying the performance of spinal codes on AWGN(Additive White Gaussian Noise)channel and in view of the existing defects of spinal code,the error bit is always concentrated in the last block,which seriously affects the performance of the whole code word bit error,and puts forward the solution to improve the performance.The first chapter introduces the research background of channel coding,code modulation and rateless code and is followed by a brief look of the characteristics of spinal codes.Chapter two analyzes the encoding and decoding structure of spinal codes.It also introduces the implementation of combining coding and modulation in detail.In the following,the hash function will be introduced.Finally,the decoding methods of spinal code's including maximum likelihood decoding and scaling-down decoding will be explained.In chapter three,we'll first make a theoretical analysis of spinal code's single symbol Euclidean distance,and analyze the relationship between single symbol and the last symbol of a code,single symbol and the code overall.We'll then calculate single symbol's function of possibility density,simulated single symbol error rate,and compare it with its block error rate.Next,we'll make a theoretical analysis of the relationship between different passes,in order to simulate and analyze the relationship between different code length and different passes,and compare-validate the theoretically estimated value and simulated value.Finally,we'll analyze how spinal code's performance is influenced by the quantification accuracy of modulated mapping,the complexity parameters of decoding and single symbol length,after which we'll simulate the relationship between spinal code's throughput and the complexity parameters of decoding plus code length.In chapter four,we propose a method of dealing with spinal code's shortcomings—adding tail symbols.First,we use the theory in chapter three to research and analyze,with depth,the gaining brought to Euclidean distance by adding tail symbols.Then,we theoretically assess the increase of block error rate brought by the given tail bits added.Finally,we simulate the gaining brought by adding tail symbols in AWGN channel,and compare it with the theoretically calculated value.In the fifth chapter,we study the application of the spinal codes over fading channel.We firstly calculate the probability desity fuction of the minimum Eculidean distance of the information symbols and the error probability of the information symbols in fading channel with known channel state information.We further formulate to maximize the code rate by minimizing the mean square error of the the error symbol probability.Correspondingly,we propose a low-complexity,sub-optimum method to improve the rate of the spinal codes over fading channel.Finally,we demonstrate the gain of the proposed method in fading channel by simulation.Chapter six concludes the thesis.This thesis is intended to provide a reference for future research by simulating the performance of spinal codes with various parameters.A scheme also is proposed to improve the transmission performance.