Research On The Technology Of Polar Coded Modulation

Polar codes have attracted the attention of researchers since they were proposed,because they belong to the capacity-achieving channel coding,which can be proved by rigorous mathematical derivation.Polar codes were derived from channel polarization,which translates the N copies of the original channel into a noisy part and noiseless part.When polar encoding,we just insert message bits into the noiseless channels,and fill the remaining channels with fixed bits.For the recursive construction of polar codes,the encoding and decoding of polar codes are simple and realizable.So polar codes have wide application prospects.In order to attain the tradeoff between the effectiveness and reliability of communication system,we apply the technique of coding and modulation into this thesis.In general,the core design concept of channel coding is adding redundant bits into codeword and protecting the valuable message,i.e.,through encoding for the valuable message,the anti-interference and error-correcting performance of the being translated message can be improved.The penalty for improving the reliability of the system by channel coding is the degradation of the effectiveness of the system.The coded modulation scheme can optimize coding and modulation synthetically to improve the performance of the communication system.In other words,we employ multilevel coding technology with flexible transmission rates and binary interleaved coded modulation to accomplish the design of coded modulation schemes,and upgrade the performance of the system.Then,basing on polar encoding and decoding theories,we analyze and research the error-correcting performance,complexity and the theoretical performance of the finite polar coded modulation system.In detail,the study can be separated into three aspects:(1)This thesis research the general equivalent channel model of binary interleaved coded modulation?the general constructing algorithm of polar codes and the design of the coded and modulation system.We make use of the similar structural characteristics between polar codes and binary interleaved coded modulation,then translate the concatenation construction of the concatenation system of multi-order modulation and polar codes into a general equivalent channel model,which consists of independent parallel channels,through considering polar coding and modulation synthetically in practical applications.We also propose a general constructing algorithm of polar codes to design the constituent polar codes for the equivalent channel model.Then we employ a bijective mapper to accomplish the modulation i.e.,binary address mapping,from coded bits to signals in constellation with Gray labeling or set partition labeling rule in different order modulations.We analyze and compare the performance of the equivalent channel model with different order modulations under different decoding algorithms.Simulation results show that the performance of our proposed schemes outperforms that of low-density parity-check codes in WiMAX standard and Turbo codes.(2)We propose an adaptive successive cancellation flip(ASCF)decoder and the modified revision of ASCF(ASCF-m)for multilevel polar coded modulation(MLPCM),which can dynamically choose decoder from different decoders for each equivalent channel,basing on the actual quality of the corresponding channel.At the same time,we propose a modified successive cancellation flip(SCF-m)decoder to improve the error-correcting performance of each component polar codes for each equivalent channel.In detail,we need to calculate two kinds of thresholds basing on the statistic property of log-likelihood ratios of the component polar codes.One kind of threshold is applied to construct the flip bit list for the SCF decoder employed in corresponding component polar codes,i.e.,SCF-m decoder.Another kind of threshold is used to generate the equivalent channel list for the ASCF decoding scheme,which guides the equivalent channel to execute the proper decoders.Through those threshold comparison decision strategies,we can dynamically allocate computational sources for different equivalent channels and obtain the tradeoff between the effectiveness and reliability of MLPCM.Experimentation demonstrates that MLPCM employing polar codes with finite coding length under the proposed ASCF and ASCF-m decoding algorithms can offer higher coding gain than that of the classical multi-stage decoding.Simultaneously,the proposed SCF-m decoding algorithm can not only improve the performance of the single component polar codes but also upgrade the total error-correcting performance of the coded and modulation system comparing with other decoders at the moderate complexity.(3)When the length of polar codes is finite,we research the theoretical characteristics of the overall capacity of the MLPCM system.We analyze and prove the capacity-achieving property of the equivalent asymmetric channels of multilevel polar coded modulation in view of scaling assuming regime,which employs some techniques of symmetric channels.Basing on the previous framework of the proof of multilevel coding modulation,we apply the scaling exponent to the equivalent asymmetric channels of multilevel polar coded modulation under the constraint of the finite coding length of component polar codes.Then,we prove that the overall capacity is still achievable under the capacity rule of the design concepts of multilevel coding.In order to accomplish reliable communication of the proposed scheme,we combine Gallager's mapping conception with source-channel coding theorems to generate the component polar codes with the optimal input distribution for each equivalent asymmetric channel.The optimal property refers to asymptotic optimization under a total variation distance measure.Finally,we describe the detail design process of multilevel polar coded modulation versus multistage decoding applying polar codes as the component codes analytically.