Investigation On Decoding And Rate Matching Techniques For Polar Codes

Polar codes,which are designed based on the idea of channel polarization,provably achieve the capacity of discrete memoryless channels,have received extensive attention since they were proposed.The specific construction and linear encoding and decoding complexity make them a promising practical application.With the development in recent years,the theoretical achievements and practical schemes of polar codes have developed rapidly.In 2016,They have been determined to be the standard coding scheme for 5G enhanced mobile broadband（e MBB）control channels.In other 5G scenarios and the upcoming next-generation mobile communication,the enhanced schemes of polar codes are still to be studied to adapt to the requirements of different scenarios.In this dissertation,we study the enhanced schemes for the two mainstream decoding algo-rithms in polar codes.Then,for the rate-matching problem,two construction schemes for arbitrary code length are proposed.Finally,a preliminary exploration of the polar codes with all alphabet sizes is discussed,which provides support for the subsequent discussion on high-order coded modulation systems.This dissertation includes the following four aspects.Firstly,two effective error detection codes,i.e.,weighted sum codes（WSC）and Internet checksum（ICS）,aided successive cancellation decoding are discussed.The error detection ability is discussed in detail.Compared with the cyclic redundancy check（CRC）,both of the detection codes have attractive error detection properties with efficient hardware imple-mentations,thereby scaling to a higher speed system.To avoid performance loss,adaptive concatenation schemes and their corresponding decoding algorithms are designed based on error detection abilities and polarization characteristics.Simulation results show that the proposed schemes achieve almost the same error performance but save check latency.In ad-dition,the WSC is also considered an early termination in belief propagation（BP）decoding.Due to termination checks being performed at each iteration,check latency is a significant part of the system latency.The simulation results demonstrate that the system latency is considerably reduced without error performance loss.Secondly,we focus on the performance improvement in the BP decoding.By analyzing the error classification and discussing the possible causes,a post-processing scheme based on code bit correction is proposed,namely,belief propagation correction（BPC）decoder.The proposed decoder corrects the identified code bit and generates the estimated codeword by additional iterations.We propose two methods for establishing the corrected set.Intuitively,the min LLR method selects indices at which the magnitude of the log-likelihood ratio is small to establish the set.This scheme can reduce decoding errors caused by channel noise.Then,combining the reliability and stopping tree,a new metric is proposed to select the corrected nodes,thus a modified BPC（MBPC）decoder is designed.The simulation shows that compared with the existing post-processing schemes,the MBPC scheme can effectively improve error performance.When code length N=2048,code rate 0.5,the MBPC decoder achieves 0.25d B performance gain when BLER=10^-5.The MBPC scheme is extended to a higher-order case to further improve the performance by a nested correction set.In addi-tion,we combine the idea of selecting the corrected nodes with noise-aided BP list decoding（Na-BPL）and discuss the performance of noise perturbation on specific code nodes.Thirdly,the rate-matching scheme is further studied.Different from the traditional punctur-ing and shortening schemes,we consider the idea of extending the code length.Using the idea of”addition”,when the code length is greater than the mother code,a two-stage po-larization（TSP）scheme based on different channel polarization and an arbitrary long polar code construction scheme based on code length decomposition,named SPCS scheme,are proposed respectively.For the TSP scheme,we first prove the polarization theorem between different channels and use this conclusion to design a two-stage polarization scheme to ob-tain performance gains.For the SPCS scheme,it is proved that the BLER performance is lower than the repetition scheme.Based on simulation and analysis results,the TSP scheme has better performance when the code length is slightly larger than the mother code.With the increase in the code length,the SPCS scheme is more suitable than the TSP scheme in the case of the longer extending code length.We demonstrate the feasibility of the scheme through theoretical proof and simulations.The simulations show that compared with the repetition scheme in the 5G standard,the proposed schemes have lower BLER performance.Lastly,a general construction scheme for all alphabet sizes is discussed,due to the advantages of nonbinary coding schemes in high order modulation.The two-dimensional transform in a q-ary discrete alphabet based on polarization mapping is a general scheme for construct-ing nonbinary codes.And the polarization mapping can be regarded as a polarization kernel matrix.In this dissertation,a specific polarization mapping based on permutation is ana-lyzed in detail.The general Monte Carlo construction scheme for the nonbinary polar codes is proposed.We propose a low-complexity information updating rule suitable for hardware implementation and design a list decoding scheme.The effectiveness of the algorithm is verified by simulation results.