Research On A Finite-Blocklength Code With High Reliability And Low Complexity-Spinal Code

With the advent of 5G communication technology,the improvement of people's demand for various life scenarios also has higher technical requirements for communication technology.For different scenarios,the channel coding method is different,and the finite-blocklength code scheme is usually used in the transmission of some important message such as transmission protocals,control signal,etc.Spinal code,as a new rate-free coding scheme,has good performance and can greatly improve the utilization of spectrum by combining coding with modulation.This paper mainly studies spinal codes under finite-blocklength code.Firstly,this paper analyzes some classic finite-blocklength code schemes.Then,a low-complexity and high-reliability spinal code based on linear matrix is proposed,by optimizing the design of linear matrix,a linear encoding matrix is given,and proved that it has the maximum euclidean distance of the modulation symbols.Meanwhile,it can reduce the complexity of encoding.Then we propose a decoding scheme based on hamming distance.Lastly,we simulate the performance of the original spinal decoding scheme.The simulation results are compared with RS code(Reed-Solomon)and LDPC(Low Density Parity Check)code.Then we study the tail symbols of spinal code,and the lower bound of error block rate is obtained by analyzing the euclidean distance of the symbols.Although tail symbols bring performance gains,they will reduce the code rate.So an improved tail symbols algorithm is proposed to compensate the reduction caused by tail symbols.Then the minimum euclidean distance analysis in single symbol scenario is given,and then extended to the minimum euclidean distance distribution among multiple symbols.The minimum euclidean distance distribution with the number of symbols increasing gradually is theoretically analyzed and verified.Firstly,the research background and the development of channel coding theory are discussed in the introduction.Then,some applications of finite-blocklength codes in 5G communication system are explained.The research target and the state of the art of spinal codes are given.In the second chapter,the encoding and decoding of RS code and LDPC code are introduced.Then the ABP(Adaptive Belief Propagation)and OSD(Ordered Statistic Decoding)algorithms and their concatenated decoding algorithms are analyzed and introduced.Lastly,the two traditional coding and decoding schemes of the spinal codes are introduced in detail.In the third chapter,the traditional low-complexity spinal codes are introduced,and the advantages and disadvantages of the scheme are studied.Then,we propose a scheme of the spinal codes based on linear matrix,then we analyse and design the selection of linear matrix.a low-complexity and high-reliability spinal code based on linear matrix is proposed.we optimize the design of linear matrix and a linear encoding matrix is given,and prove that it has the maximum euclidean distance of the modulation symbols.Then we simulate and analyze the original spinal code and the proposed scheme in terms of performance and complexity.Lastly we compare and analyze the performance of RS code and LDPC code with finite-blocklength.In chapter 4,firstly,the minimum euclidean distance between single symbols is analyzed.Then we analyze the gains brought by tail symbol and the reduction caused by tail symbols and the principle that tail symbols can bring gains to spinal codes,and we give the lower bound of error probability of spinal codes through the minimum euclidean distance and improve the tail symbol algorithm to design it without increasing complexity and reducing decoding performance.It compensates the reduction caused by tail symbols,and the minimum euclidean distance distribution among multiple symbols is obtained.At the same time,the distribution of euclidean distance when the number of symbols increases is theoretically analyzed and verified.In the fifth chapter,this paper summarizes the content of this study,and summarizes the research content and direction,as well as the limitations and shortcomings of the results.Finally,the prospect of the research content is prospected.