Research On Encoding And Decoding Algorithms For Polar Codes

Polar codes are a kind of provably capacity-achieving codes.Compared with other existing error-correcting codes,polar codes have a regular encoding structure,an explicit construction method,and low complexities of encoding and decoding algorithms.Polar codes also have the advantages of rich algebraic structure and excellent analytical characteristics.Polar codes are considered to have potential applications in the field such as the 5^th generation mobile communication,digital storage and optical network.Hence,polar codes have become an attractive research area in the modern channel coding field.In this dissertation,the performance optimization of decoding algorithm and the construction of relaxed polarization for polar codes are investigated.Some main results are obtained and summarized as follows:1.Based on the statistical analysis of single-bit errors and 2-bit errors,a successive cancellation?SC?multibit-flipping decoding algorithm is proposed.Compared with the SC single-bit-flipping decoding,the proposed scheme can obtain better performance gains for polar codes.Compared with the CRC-SCL decoding by exploring multiple paths simultaneously,the proposed scheme has a lower space complexity.Simulation shows that for polar codes with short or moderate blocklength,the performance of the proposed decoder can approach that of CRC-SCL decoding with lower decoding complexity in high SNR regions.2.The influence of unreliable information bits on the decoding performance of polar codes by SC is investigated.An algorithm of CRC-aided SC partial list decoding is proposed.By using the reliable frozen bits to transimit the the redundant bits generated by CRC for the unreliable information bits,the proposed scheme can improve the reliability of the information-bit transmission.Since the list decoding is used only between the chosen bits,the proposed scheme can reduce the complexity of CRC-SCL decoding and have almost the same decoding performance but without loss of rate.3.It is shown that the sparsity of a dense parity-check matrix can be decreased by using the Gauss elimination iteratively.With the aid of the idea,enhanced belief propagation?BP?decoding of polar codes by parity-check matrix adaptation is proposed.By reducing significantly row weight and column weight,the proposed scheme improves the convergence rate of polar BP and decreases the error rate of decoding.Compared with the CRC-SCL of the list size 32,the proposed decoder can perform better under a lower average decoding complexity.4.An efficient optimization scheme of the interleaved Reed-Solomon polar concatenated codes?RS-Polar?is proposed with the aid of repetition codes.By using the unreliable information bits and reliable frozen bits,the repetition codes are constructed to be outer codes and concatenated with the inner polar codes of RS-Polar codes.Since the proposed scheme can improve the reliability of information-bits transmission,it can enhance the error-correcting capability of the inner polar codes and the performance of the original RS-Polar.5.By investigating the characteristic of the encoding structure for polar codes,we propose a computational method of the subchannel reliabilities in the relaxed polarization based on the Gauss approximation,and a construction algorithm of the generator matrix for relaxed polar codes.Compared with the Gauss approximation used in the full polarization,the proposed computational method can choose the almost same indices of information bits.Using the proposed construction algorithm for generator matrices,the relaxed polar codes can obtain the almost same performance as that of the full polar codes under SC decoding.