Research On The Decoding Algorithm Of Polarization Codes

In order to pursue higher transmission rates and higher reliability of communication requirements,the fifth generation of mobile communication systems that meet such requirements will inevitably become the mainstream of communication development.The polar code coding scheme proposed by E.Arikan is an innovation in the coding field.Because of its unique coding structure and the use of mathematical iterative formulas and the lower computational complexity than Turbo codes and Low Density Parity Checks,the research of this code has become a hotspots for domestic and foreign scholar.This paper mainly studies the decoding algorithm of polar code,The premise of studying the decoding algorithm is a thorough understanding of the encoding of the polar code.Therefore,in the research process of this article,the coding aspect also becomes a part of the workload,and the focus is still on the research of decoding.First,it summarizes the current state of development of polar codes.On the basis of reading a large number of documents,understand the theory of channel polarization,and being verified the polarization phenomenon on the platform of Matlab2017.Based on the polarization phenomenon which be described above,Mathematical formulas to derive the code generation matrix,the generation methods of bit by bit,and the generation methods of column-by-column that extended to long codes,I studied the BEC method and the Monte-Carlo method and the Gaussian approximation method,and analyzed their influence on polarization coding efficiency.Secondly,explore the decoding principle of SC decoding algorithm.Combine the butterfly structure with the butterfly formula,Introduce LLR for the accuracy"underflow"problem of traditional SC decoding algorithms,Analyze the data storage structure of LLR values,design the SC decoding flow chart,and design the entire polar code encoding and decoding system program.The time-computational complexity and spatial space complexity areO(NlogN)andO(N)respectively.At the same time,study the SCL decoding algorithm and change hard decisions to soft decisions,The reserved path is determined by the L value,and the path metric PM is the parameter of the selected path,On the basis of the SC decoding program,function modules such as path copying,path deletion,and optimal path selection are added.Set L,Running the simulation to obtain the performance comparison under different path widths,The time complexity and spatial space complexity of the algorithm are O(L?NlogN)andO(L?N)respectively.The bit error rate and block error rate of the decoding curve are significantly lower than the SC decoding algorithm.Finally,Study the CA-SCL algorithm,sacrifice the coding efficiency to reduce the computational complexity,add the L-bit CRC,and compare the simulation performance chart in Matlab2017.The repeated calculation of the LLR value of this algorithm makes the computational complexityO(N~2),To optimize the algorithm,an"Lazy Copy"algorithm was introduced to simulate and compare the performance of different decoding algorithms,and the performance of the decoding algorithm was gradually improved.