Research And Improvement On Decoding Algorithm Of Polar Codes

Polar codes represent an emerging class of error-correcting codes with power to approach the capacity of a discrete memoryless channel.Apart from its low encoding and decoding complexity,polar codes have attracted much attention since it can achieve optimal performance in many communication scenarios like wireless communication systems.The SC decoding of polar codes can be regarded as a greedy search algorithm over the code tree.Between the two branches associated with an information bit at certain level,only the one with the larger probability is selected for further processing.Whenever a bit is wrongly determined,it becomes impossible to correct it in the future decoding procedure.However,unlike SC where only one path is reserved after processing at each level,the SCL can be regarded as a breadth-first search algorithm and allows a maximum of L candidate paths to be further explored.To further improve the performance of polar codes,CRC-aided SCL decoding algorithm,called CA-SCL,have been proposed.They belong to the enhancement algorithm of SC.In this paper,the SC,SCL and CA-SCL algorithms are simulated.Iterative decoding is a common method in many decoding schemes.The main difficulty in directly applying iterative decoding techniques to polar codes is that the parity-check matrix of a polar code is in general not sparse.In order to deal with such dense parity-check matrices,proposed scheme is to adapt the parity-check matrix at each iteration according to the bit reliabilities such that the unreliable bits correspond to a sparse submatrix.The SPA(sumproduct algorithm)is then applied to the adapted parity-check matrix.In SC decoding,the first erroneous decision is always caused by the channel noise since there are no previous errors,but the subsequent bit erroneous decisions can be caused by error propagation due to previous erroneous bit decisions.In this paper,through the simulations,the proportion of an error which leads to the entire codeword error is very high.Hence,it is critical to find the location where the first error occurred and correct it without allowing it to affect any future bit decisions.According to the phenomenon of error propagation,improved SC decoding algorithm based on bit flipping and improved SCL decoding algorithm based on bit flipping are proposed.As can be seen from the results of the simulation,the performance of the improved SC decoding algorithm based on bit flipping is better than SC algorithm and the performance of the improved SCL decoding algorithm based on bit flipping is better than CA-SCL algorithm.Although these two algorithms have loss in complexity,the performance has improved.