Research On Polar Coding And Its BICM Implementations

Polar codes are the first error correcting codes that ever provably can achieve the symmetric capacity of any given binary-input discrete memoryless channel.It has been developing rapidly in less than ten years,and has been adopted as channel coding for control information for enhanced mobile broadband scenario in 5G.Based on the encoding and decoding algorithm of polar codes,we study the puncturing,hybrid auto-matic repeat request(HARQ)and bit interleaved coded modulation(BICM)of polar codes,and explore the application of polar codes in multicolor visible light communication systems.First of all,the paper will introduce the encoding and decoding algorithm of polar codes.In the respect of encoding,we start from the generator matrix of polar codes,introducing the theory of channel combining and splitting.It combines algorithm with theory to deepen the understanding of polar codes.We also give different methods to select the positions of information bits in the source block of polar codes.In the respect of decoding,we introduce various decoding algorithms including successive cancellation(SC),belief prop-agation(BP)and list decoding.We give the core fomula of these algorithms,and analyze the complexity and latency.By means of simulation,the influence of code length and code rate on the performance of polar codes is analyzed,and the performance and factors of different decoding algorithms are compared.Secondly,the paper will introduce and compare the puncturing schemes and HARQ schemes of polar codes.In the respect of puncturing,it is divided into traditional puncturing and shortening.The traditional puncturing mainly includes exhaustive search approach which has optimal performance,progressive search approach which is in a nested way,and grouping progressive search approach which has simplified calcula-tion.For shortening,we reveal its essence of the sacrifice of encoding performance and give its optimization conditions.In the respect of HARQ,a general scheme is proposed for traditional puncturing,and the schemes of incremental freezing and incremental length are introduced for shortening.By means of simulation,the performance of the different schemes are compared and analyzed,making preparations for further study.Then,the design of BICM for polar codes is discussed in this paper.According to the framework of en-coding,puncturing,interleaving,modulation,channel,demodulation,deinterleaving and decoding,a system model of bit interleaved polar coded modulation is built.The encoding schemes of polar codes are reviewed and extended,and the interleaving algorithms suitable for polar codes are discussed.With the theory of den-sity evolution,the recursive formula for message passing of polar codes and the block error rate formula are derived using Gaussian approximation.We traverse all the interleaving patterns on a short block polar codes in the high order modulation.Combining the theoretical calculation with simulation,we suspect the optimal interleaving pattern and conclude the design of BICM for polar codes.By means of simulation,our design of BICM for polar codes is verified from the aspect of different code rates,different code lengths and different modulation orders.And it can been seen that our design outperforms the standard polar codes with random interleaver at least 0.5 dB at a BLER of 10-2.Finally,the paper will discuss the design of polar codes for multicolor visible light communication(VLC)systems.An RGBA-LED-based VLC system model with polar coding is presented.Using the design signal-to-noise ratio(SNR)and the equivalent channel matrix of the system,we calculate the signal-to-interference-plus-noise ratios(SINRs)of four color channels.The recursive formula of channel polarization for four color channels is given,and the initial parameter of channel polarization is defined by the functions of the SINRs of four color channels.The design-SNR is used as a design variable,by changing which the optimal scheme of polar codes can be obtained.By means of simulation,our design is verified from the aspect of different code rates and different decoders.It can been seen that our design outperforms the standard polar codes at least 5 dB at a BLER of 10-3 in the RGBA-LED-based VLC system.Meanwhile,without the optimization of other modules,our design is superior to the standard polar codes with a random interleaver in the RGBA-LED-based VLC system,and better than LDPC codes in the RGBA-LED-based VLC system as well.