Research On Improved Decoding Algorithm Of Polar Code And Reed-Muller Code

Polar codes are the only encoding method that can realize symmetric capacity in any binary input discrete channel.Channel polarization theory is used to implement a specific encoding that method which is similar to algebraic encoding.Polar codes adopt a brand-new encoding method which makes it simpler in structure and better in performance.These features make the Polar code the encoding method on the control channel of 5G communication.The belief propagation(BP)iterative decoding algorithm is applied to the decoding process of Polar codes for its parallel processing.For the BP decoding algorithm with excellent decoding performance but long decoding time,this paper proposes an improved BP decoding algorithm based on early terminating iteration criterion of the absolute values difference for the likelihood firstly.The simulation results illustrate that the early-terminating iteration criterion proposed in this paper reduces the computational complexity,thereby reducing the decoding delay and energy consumption effectively.The majority logic soft decision decoding algorithm is applied to the decoding of Reed-Muller(RM)code owing to its excellent performance.Dealing with the problem of lacking error control in large number logic soft decision decoding algorithm of binary RM codes,this paper presents the calculation of the number of the most unreliable positions in the receiving sequence of the highest order information bits of the RM codes secondly.An improved large number logic soft decision decoding algorithm based on error probability is proposed to deal with these unreliable positions in the received sequence.The simulation results show that compared with the traditional soft-decision decoding algorithm,the improved decoding algorithm proposed in this paper reduces the bit error rate of RM code,improves the decoding performance and error correction performance.The construction method of the Polar code generation matrix is similar to the hierarchical structure of the RM code,the decoding performance and decoding time of RM and Polar codes of the same code length and code rate are compared under the successive cancellation decoding algorithm and the BP iterative algorithm without iteration finally.The simulation results show that the SC soft decision decoding algorithm can decode the RM code,and the SC decoding time is reduced by 98.98% compared with the BP decoding algorithm.This paper provides a feasible way to improve the decoding efficiency of Polar and RM code,so that Polar and RM code can obtain more research results and have a greater breakthrough in practical applications.