Research On Decoding And Multilevel Coded Modulation For Polar Codes

As the first class of provably capacity-achieving channel codes under any binary-input discrete memoryless channel,polar codes have gained much attention due to their explicit construction and quite low complexity of encoding as well as decoding.However,the error correcting performance of polar codes at low-to-moderate block lengths under classic SC decoding turns out to be inferior.To improve the performance of the suboptimal decoding method,plenty of improved decoding algorithms have been proposed,such as SCL,which suffers from high complexity.After that,many modifications have been investigated to reduce the complexity greatly.Additionally,the requirement for the combination of binary polar codes and high order modulation is also evident for increasing the spectral efficiency.In this thesis,we investigate the decoding algorithms to improve the performance or reduce the complexity,and provide novel polar-coded modulation approaches based on multilevel coding(MLC).Based on the analysis of the encoding structure and classic methods for constructing polar codes,the effect of the design signal-to-noise ratio(SNR)deviation on the performance of polar codes is studied and an adaptive transmission scheme based on Gaussian approximation is then proposed to improve the performance under non-ideal channel conditions.A PC aided Multi-CRC-SCL decoding algorithm is proposed based on multi-CRC polar codes to improve the decoding performance of polar codes at low-to-moderate block lengths with the help of concatenating PC bits,which penalizes incorrect paths and reduces the probability of pruning the correct path,while maintaining the ability of early stopping.In addition,to get a better trade-off between the computation complexity and frame error rate(FER)performance,a novel decoding algorithm called segmented CRC aided SCRL is proposed for significant reduction of computation complexity and memory size with negligible performance loss.We show that by reducing the size of list when completing the CRC check on each sub-block and allocating CRC bits to the most reliable positions,useless paths can be pruned early and significant reduction of decoding complexity can be achieved while maintaining good performance.A multilevel polar-coded modulation scheme based on the same bit error rate(BER)goal of each bit level is proposed to improve the performance of polar-coded modulation by utilizing the set-partitioning-labeling-based MLC modulation.Furthermore,we provide a multilevel polar-coded modulation scheme keeping the most significant bit(MSB)prior based on the capacity distribution of virtual bit channels.By sorting the symmetric capacity of all bit channels together and allocating various rates of the component codes for each bit level following capacity-rule and the MSB-first rule,the proposed scheme can improve the performance greatly.Moreover,a decoder-matching multilevel polar-coded modulation transmission scheme is proposed to reduce the decoding complexity while maintaining good performance by properly allocating list sizes for each decoder corresponding to the bit levels and multiplying the same CRC encoder and decoder.We show that both the computation complexity and required memory resource are reduced.