Aiming at the problem that the bit error rate(BER)of asymmetrically clipped optical orthogonal frequency division multiplexing(ACO-OFDM)space optical communication system is significantly affected by different turbule...Aiming at the problem that the bit error rate(BER)of asymmetrically clipped optical orthogonal frequency division multiplexing(ACO-OFDM)space optical communication system is significantly affected by different turbulence intensities,the deep learning technique is proposed to the polarization code decoding in ACO-OFDM space optical communication system.Moreover,this system realizes the polarization code decoding and signal demodulation without frequency conduction with superior performance and robustness compared with the performance of traditional decoder.Simulations under different turbulence intensities as well as different mapping orders show that the convolutional neural network(CNN)decoder trained under weak-medium-strong turbulence atmospheric channels achieves a performance improvement of about 10^(2)compared to the conventional decoder at 4-quadrature amplitude modulation(4QAM),and the BERs for both 16QAM and 64QAM are in between those of the conventional decoder.展开更多
The beyond fifth-generation Internet of Things requires more capable channel coding schemes to achieve high-reliability,low-complexity and lowlatency communications.The theoretical analysis of error-correction perform...The beyond fifth-generation Internet of Things requires more capable channel coding schemes to achieve high-reliability,low-complexity and lowlatency communications.The theoretical analysis of error-correction performance of channel coding functions as a significant way of optimizing the transmission reliability and efficiency.In this paper,the efficient estimation methods of the block error rate(BLER)performance for rate-compatible polar codes(RCPC)are proposed under several scenarios.Firstly,the BLER performance of RCPC is generally evaluated in the additive white Gaussian noise channels.That is further extended into the Rayleigh fading channel case using an equivalent estimation method.Moreover,with respect to the powerful decoder such as successive cancellation list decoding,the performance estimation is derived analytically based on the polar weight spectrum and BLER upper bounds.Theoretical evaluation and numerical simulation results show that the estimated performance can fit well the practical simulated results of RCPC under the objective conditions,verifying the validity of our proposed performance estimation methods.Furthermore,the application designs of the reliability estimation of RCPC are explored,particularly in the advantages of the signal-to-noise(SNR)estimation and throughput efficiency optimization of polar coded hybrid automatic repeat request.展开更多
In this paper,a sparse graph neural network-aided(SGNN-aided)decoder is proposed for improving the decoding performance of polar codes under bursty interference.Firstly,a sparse factor graph is constructed using the e...In this paper,a sparse graph neural network-aided(SGNN-aided)decoder is proposed for improving the decoding performance of polar codes under bursty interference.Firstly,a sparse factor graph is constructed using the encoding characteristic to achieve high-throughput polar decoding.To further improve the decoding performance,a residual gated bipartite graph neural network is designed for updating embedding vectors of heterogeneous nodes based on a bidirectional message passing neural network.This framework exploits gated recurrent units and residual blocks to address the gradient disappearance in deep graph recurrent neural networks.Finally,predictions are generated by feeding the embedding vectors into a readout module.Simulation results show that the proposed decoder is more robust than the existing ones in the presence of bursty interference and exhibits high universality.展开更多
The construction of polar codes in corre-lated block fading channels is still an open issue to be solved.In this paper,to explicitly reveal the impact of correlation on error performance of polar coded diver-sity comm...The construction of polar codes in corre-lated block fading channels is still an open issue to be solved.In this paper,to explicitly reveal the impact of correlation on error performance of polar coded diver-sity communication systems,an integrated framework has been established to analyze the theoretical error performance of polar codes in correlated block fading channels.First,the upper bound on error probabil-ity of polarized channels is derived based on split po-lar spectrum,which is fully determined by covariance channel matrix as well as the block-wise weight distri-bution of the corresponding polar subcode.Further,to facilitate practical implementations,we design a con-struction metric named polarized correlation weight(PCW)to generate polar codes in correlated block fad-ing channels.Finally,simulation results on block error rate indicate that the proposed metric can exhibit both diversity gain and coding gain compared to the con-ventional methods under successive cancellation de-coding.展开更多
Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulti...Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulting in high decoding complexity and latency.To alleviate this issue,we incorporate the LDPC-CRC-Polar coding scheme with BPBF and propose an improved belief propagation decoder for LDPC-CRC-Polar codes with bit-freezing(LDPCCRC-Polar codes BPBFz).The proposed LDPCCRC-Polar codes BPBFz employs the LDPC code to ensure the reliability of the flipping set,i.e.,critical set(CS),and dynamically update it.The modified CS is further utilized for the identification of error-prone bits.The proposed LDPC-CRC-Polar codes BPBFz obtains remarkable error correction performance and is comparable to that of the CA-SCL(L=16)decoder under medium-to-high signal-to-noise ratio(SNR)regions.It gains up to 1.2dB and 0.9dB at a fixed BLER=10-4compared with BP and BPBF(CS-1),respectively.In addition,the proposed LDPC-CRC-Polar codes BPBFz has lower decoding latency compared with CA-SCL and BPBF,i.e.,it is 15 times faster than CA-SCL(L=16)at high SNR regions.展开更多
In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete mem...In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.展开更多
Belief propagation list(BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL(CA-SCL) decoding.In this work, an improved s...Belief propagation list(BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL(CA-SCL) decoding.In this work, an improved segmented belief propagation list decoding based on bit flipping(SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the errorcorrection performance of BPL decoding for medium and long codes. It is more than 0.25 d B better than the state-of-the-art BPL decoding at a block error rate(BLER) of 10^(-5), and outperforms CA-SCL decoding in the low signal-to-noise(SNR) region for(1024, 0.5)polar codes.展开更多
Power line communication(PLC)has the potential to become the preferred technique for providing broadband communication to homes and offices with advantage of eliminating the need for new wiring infrastructure and redu...Power line communication(PLC)has the potential to become the preferred technique for providing broadband communication to homes and offices with advantage of eliminating the need for new wiring infrastructure and reducing the cost.But it suffers from the impulsive noise because it introduces significant time variance into the power line channel.In this paper,a polar codes based orthogonal frequency division multiplexing(OFDM)PLC system is proposed to deal with the impulsive noise and thereby improve the transmission performance.Firstly,the impulsive noise is modelled with a multi-damped sine function by analyzing the time behavior of impulse events.Then the polar codes are used to combat the impulsive noise of PLC channel,and a low complexity bit-flipping decoding method based on CRC-aided successive cancellation list(CA-SCL)decoding algorithm is proposed.Simulations evaluate the proposed decoding algorithm and the results validate the suggested polar codes based OFDM-PLC scheme which can improve the BER performance of PLC with impulsive interference.展开更多
After the pursuit of seventy years,the invention of polar codes indicates that we have found the first capacity-achieving coding with low complexity construction and decoding,which is the great breakthrough of the cod...After the pursuit of seventy years,the invention of polar codes indicates that we have found the first capacity-achieving coding with low complexity construction and decoding,which is the great breakthrough of the coding theory in the past two decades.In this survey,we retrospect the history of polar codes and summarize the advancement in the past ten years.First,the primary principle of channel polarization is investigated such that the basic construction,coding method and the classic successive cancellation(SC)decoding are reviewed.Second,in order to improve the performance of the finite code length,we introduce the guiding principle and conclude five design criteria for the construction,design and implementation of the polar code in the practical communication system based on the exemplar schemes in the literature.Especially,we explain the design principle behind the concatenated coding and rate matching of polar codes in 5G wireless system.Furthermore,the improved SC decoding algorithms,such as SC list(SCL)decoding and SC stack(SCS)decoding etc.,are investigated and compared.Finally,the research prospects of polar codes for the future 6G communication system are explored,including the optimization of short polar codes,coding construction in fading channels,polar coded modulation and HARQ,and the polar coded transmission,namely polar processing.Predictably,as a new coding methodology,polar codes will shine a light on communication theory and unveil a revolution in transmission technology.展开更多
Polar codes have become increasingly popular recently because of their capacity achieving property.In this paper,a memory efficient stage-combined belief propagation(BP) decoder design for polar codes is presented.Fir...Polar codes have become increasingly popular recently because of their capacity achieving property.In this paper,a memory efficient stage-combined belief propagation(BP) decoder design for polar codes is presented.Firstly,we briefly reviewed the conventional BP decoding algorithm.Then a stage-combined BP decoding algorithm which combines two adjacent stages into one stage and the corresponding belief message updating rules are introduced.Based on this stage-combined decoding algorithm,a memory-efficient polar BP decoder is designed.The demonstrated decoder design achieves 50%memory and decoding latency reduction in the cost of some combinational logic complexity overhead.The proposed decoder is synthesized under TSMC 45 nm Low Power CMOS technology.It achieves 0.96 Gb/s throughput with 14.2mm^2 area when code length N=2^(16)which reduces 51.5%decoder area compared with the conventional decoder design.展开更多
Recently,a generalized successive cancellation list(SCL)decoder implemented with shiftedpruning(SP)scheme,namely the SCL-SP-ωdecoder,is presented for polar codes,which is able to shift the pruning window at mostωtim...Recently,a generalized successive cancellation list(SCL)decoder implemented with shiftedpruning(SP)scheme,namely the SCL-SP-ωdecoder,is presented for polar codes,which is able to shift the pruning window at mostωtimes during each SCL re-decoding attempt to prevent the correct path from being eliminated.The candidate positions for applying the SP scheme are selected by a shifting metric based on the probability that the elimination occurs.However,the number of exponential/logarithm operations involved in the SCL-SP-ωdecoder grows linearly with the number of information bits and list size,which leads to high computational complexity.In this paper,we present a detailed analysis of the SCL-SP-ωdecoder in terms of the decoding performance and complexity,which unveils that the choice of the shifting metric is essential for improving the decoding performance and reducing the re-decoding attempts simultaneously.Then,we introduce a simplified metric derived from the path metric(PM)domain,and a custom-tailored deep learning(DL)network is further designed to enhance the efficiency of the proposed simplified metric.The proposed metrics are both free of transcendental functions and hence,are more hardware-friendly than the existing metrics.Simulation results show that the proposed DL-aided metric provides the best error correction performance as comparison with the state of the art.展开更多
Non-orthogonal multiple access(NOMA)is deemed to have a superior spectral efficiency and polar codes have became the channel coding scheme for control channel of enhanced mobile broadband(eMBB)in the fifth generation(...Non-orthogonal multiple access(NOMA)is deemed to have a superior spectral efficiency and polar codes have became the channel coding scheme for control channel of enhanced mobile broadband(eMBB)in the fifth generation(5G)communication systems.In this paper,NOMA combined with polar codes is used to achieve secure transmission.Both degraded wiretap channel and non-degraded wiretap channel are considered,where an eavesdropper intercepts the communication between base station(BS)and users.For the degraded wiretap channel scenario,a secure polar encoding scheme is proposed in NOMA systems with power allocation to achieve the maximum secrecy capacity.With regard to the nondegraded wiretap channel,a polar encoding scheme with multiple-input-single-output(MISO)system is proposed,where artificial noise is generated at BS to confuse the eavesdropper’s channel via transmit beamforming.The security and the secure rate are employed respectively in order to measure the secrecy performance.We prove that the proposed schemes for each scenario can achieve the secure rate and can transmit the signal securely and reliably.The simulation results show that the eavesdropper hardly decoding the secure signal when the legitimate receiver can decode the signal with very low block error rate(BLER).展开更多
In this paper,we propose an arbitrary decode-forward single-relay scheme for finite blocklength polar codes,which can be applied to the general symmetric discrete memoryless relay channel with orthogonal receiver comp...In this paper,we propose an arbitrary decode-forward single-relay scheme for finite blocklength polar codes,which can be applied to the general symmetric discrete memoryless relay channel with orthogonal receiver components.The relay node decodes the received message.The relay node selectively re-encodes the message and transmits it to the destination node.Furthermore,in order to minimize the upper-bound of the block error probability,we propose a selection strategy to decide the proper re-encoded bit set by the relay.Simulation results are presented to illustrate the improvement in decoding performance of the proposed scheme compared to conventional relay schemes in both additive white Gaussian noise(AWGN)channel and Rayleigh fading channel(RFC).展开更多
The increasing data traffic rate of wireless communication systems forces the development of new technologies mandatory.Providing high data rate,extremely low latency and improvement on quality of service are the main...The increasing data traffic rate of wireless communication systems forces the development of new technologies mandatory.Providing high data rate,extremely low latency and improvement on quality of service are the main subjects of next generation 5G wireless communication systems which will be in the people’s life in the years of 2020.As the newest and first mathematically proven forward error correction code,polar code is one of the best candidates among error correction methods that can be employed for 5G wireless networks.The aim of this tutorial is to show that belief propagation decoding of polar codes can be a promising forward error correction technique in upcoming 5G frameworks.First,we survey the novel approaches to the belief propagation based decoding of polar codes and continue with the studies about the simplification of these decoders.Moreover,early detection and termination methods and concept of scheduling are going to be presented throughout the manuscript.Finally,polar construction algorithms,error types in belief propagation based decoders and hardware implementations are going to be mentioned.Overall,this tutorial proves that the BP based decoding of polar codes has a great potential to be a part of communication standards.展开更多
To remove the restriction on code length of polar codes,this paper proposes a construction scheme,called stepwise polar codes,which can gen-erate arbitrary-length polar codes.The stepwise polar codes are generated by ...To remove the restriction on code length of polar codes,this paper proposes a construction scheme,called stepwise polar codes,which can gen-erate arbitrary-length polar codes.The stepwise polar codes are generated by sub-polar codes with different code lengths.To improve coding performance,sub-polar codes are united by polarization effect priority algorithm,which can reduce the number of in-completely polarized channels.Then,the construction method of the generator matrix of the stepwise po-lar code is presented.Furthermore,we prove that the proposed scheme has lower decoding complexity than punctured,multi-kernel polar codes.Simulation results show that the proposed method can achieve similar decoding performance compared with the conventional punctured polar codes,rate-compatible punctured polar code,PC-short and asymmetric polar codes(APC)when code length N=48 and 72,respectively.展开更多
Mission critical Machine-type Communication(mcMTC),also referred to as Ultra-reliable Low Latency Communication(URLLC),has become a research hotspot.It is primarily characterized by communication that provides ultra-h...Mission critical Machine-type Communication(mcMTC),also referred to as Ultra-reliable Low Latency Communication(URLLC),has become a research hotspot.It is primarily characterized by communication that provides ultra-high reliability and very low latency to concurrently transmit short commands to a massive number of connected devices.While the reduction in physical(PHY)layer overhead and improvement in channel coding techniques are pivotal in reducing latency and improving reliability,the current wireless standards dedicated to support mcMTC rely heavily on adopting the bottom layers of general-purpose wireless standards and customizing only the upper layers.The mcMTC has a significant technical impact on the design of all layers of the communication protocol stack.In this paper,an innovative bottom-up approach has been proposed for mcMTC applications through PHY layer targeted at improving the transmission reliability by implementing ultra-reliable channel coding scheme in the PHY layer of IEEE 802.11a standard bearing in mind short packet transmission system.To achieve this aim,we analyzed and compared the channel coding performance of convolutional codes(CCs),low-density parity-check(LDPC)codes,and polar codes in wireless network on the condition of short data packet transmission.The Viterbi decoding algorithm(VA),logarithmic belief propagation(Log-BP)algorithm,and cyclic redundancy check(CRC)successive cancellation list(SCL)(CRC-SCL)decoding algorithm were adopted to CC,LDPC codes,and polar codes,respectively.Consequently,a new PHY layer for mcMTC has been proposed.The reliability of the proposed approach has been validated by simulation in terms of Bit error rate(BER)and packet error rate(PER)vs.signal-to-noise ratio(SNR).The simulation results demonstrate that the reliability of IEEE 802.11a standard has been significantly improved to be at PER=10−5 or even better with the implementation of polar codes.The results also show that the general-purpose wireless networks are prominent inproviding short packet mcMTC with the modification needed.展开更多
The error correction performance of Belief Propagation(BP)decoding for polar codes is satisfactory compared with the Successive Cancellation(SC)decoding.Nevertheless,it has to complete a fixed number of iterations,whi...The error correction performance of Belief Propagation(BP)decoding for polar codes is satisfactory compared with the Successive Cancellation(SC)decoding.Nevertheless,it has to complete a fixed number of iterations,which results in high computational complexity.This necessitates an intelligent identification of successful BP decoding for early termination of the decoding process to avoid unnecessary iterations and minimize the computational complexity of BP decoding.This paper proposes a hybrid technique that combines the“paritycheck”with the“G-matrix”to reduce the computational complexity of BP decoder for polar codes.The proposed hybrid technique takes advantage of the parity-check to intelligently identify the valid codeword at an early stage and terminate the BP decoding process,which minimizes the overhead of the G-matrix and reduces the computational complexity of BP decoding.We explore a detailed mechanism incorporating the parity bits as outer code and prove that the proposed hybrid technique minimizes the computational complexity while preserving the BP error correction performance.Moreover,mathematical formulation for the proposed hybrid technique that minimizes the computation cost of the G-matrix is elaborated.The performance of the proposed hybrid technique is validated by comparing it with the state-of-the-art early stopping criteria for BP decoding.Simulation results show that the proposed hybrid technique reduces the iterations by about 90%of BP decoding in a high Signal-to-Noise Ratio(SNR)(i.e.,3.5~4 dB),and approaches the error correction performance of G-matrix and conventional BP decoder for polar codes.展开更多
The soft cancellation decoding of polar codes achieves a better performance than the belief propagation decoding with lower computational time and space complexities.However,because the soft cancellation decoding is b...The soft cancellation decoding of polar codes achieves a better performance than the belief propagation decoding with lower computational time and space complexities.However,because the soft cancellation decoding is based on the successive cancellation decoding,the decoding efficiency and performance with finite-length blocks can be further improved.Exploiting the idea of the successive cancellation list decoding,the soft cancellation decoding can be improved in two aspects:one is by adding branch decoding to the error-prone information bits to increase the accuracy of the soft information,and the other is through using partial iterative decoding to reduce the time and computational complexities.Compared with the original method,the improved soft cancellation decoding makes progress in the error correction performance,increasing the decoding efficiency and reducing the computational complexity,at the cost of a small increase of space complexity.展开更多
Soft decode-and-forward(DF) can combine the advantages of both amplify-and-forward and hard DF in relay channels. In this paper, we propose a low-complexity soft DF scheme based on polar codes, which features two key ...Soft decode-and-forward(DF) can combine the advantages of both amplify-and-forward and hard DF in relay channels. In this paper, we propose a low-complexity soft DF scheme based on polar codes, which features two key techniques: a low-complexity cyclic redundancy check(CRC) aided list successive cancellation(CALSC) decoder and a soft information calculation method. At the relay node, a low-complexity CALSC decoder is designed to reduce the computational complexity by adjusting the list size according to the reliabilities of decoded bits. Based on the path probability metric of the CALSC decoder, we propose a method to compute the soft information of the decoded bits in CALSC. Simulation results show that our proposed scheme outperforms the soft DF based on low-density parity-check codes and the soft DF with belief propagation or soft cancellation decoder, especially in the case when the source-relay channel is at the high signal-to-ratio region.展开更多
Polar codes represent one of the major breakthroughs in 5G standard,and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list...Polar codes represent one of the major breakthroughs in 5G standard,and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list(SCL)decoding algorithm.However,the SCL algorithm suffers from a large amount of memory overhead.This paper proposes an adaptive simplified decoding algorithm for multiple cyclic redundancy check(CRC)polar codes.Simulation results show that the proposed method can reduce the decoding complexity and memory space.It can also acquire the performance gain in the low signal to noise ratio region.展开更多
基金supported by the National Natural Science Foundation of China(No.12104141).
文摘Aiming at the problem that the bit error rate(BER)of asymmetrically clipped optical orthogonal frequency division multiplexing(ACO-OFDM)space optical communication system is significantly affected by different turbulence intensities,the deep learning technique is proposed to the polarization code decoding in ACO-OFDM space optical communication system.Moreover,this system realizes the polarization code decoding and signal demodulation without frequency conduction with superior performance and robustness compared with the performance of traditional decoder.Simulations under different turbulence intensities as well as different mapping orders show that the convolutional neural network(CNN)decoder trained under weak-medium-strong turbulence atmospheric channels achieves a performance improvement of about 10^(2)compared to the conventional decoder at 4-quadrature amplitude modulation(4QAM),and the BERs for both 16QAM and 64QAM are in between those of the conventional decoder.
基金supported by National Natural Science Foundation of China(No.62201596)Research Planning Project of National University of Defense Technology(ZK22-45).
文摘The beyond fifth-generation Internet of Things requires more capable channel coding schemes to achieve high-reliability,low-complexity and lowlatency communications.The theoretical analysis of error-correction performance of channel coding functions as a significant way of optimizing the transmission reliability and efficiency.In this paper,the efficient estimation methods of the block error rate(BLER)performance for rate-compatible polar codes(RCPC)are proposed under several scenarios.Firstly,the BLER performance of RCPC is generally evaluated in the additive white Gaussian noise channels.That is further extended into the Rayleigh fading channel case using an equivalent estimation method.Moreover,with respect to the powerful decoder such as successive cancellation list decoding,the performance estimation is derived analytically based on the polar weight spectrum and BLER upper bounds.Theoretical evaluation and numerical simulation results show that the estimated performance can fit well the practical simulated results of RCPC under the objective conditions,verifying the validity of our proposed performance estimation methods.Furthermore,the application designs of the reliability estimation of RCPC are explored,particularly in the advantages of the signal-to-noise(SNR)estimation and throughput efficiency optimization of polar coded hybrid automatic repeat request.
文摘In this paper,a sparse graph neural network-aided(SGNN-aided)decoder is proposed for improving the decoding performance of polar codes under bursty interference.Firstly,a sparse factor graph is constructed using the encoding characteristic to achieve high-throughput polar decoding.To further improve the decoding performance,a residual gated bipartite graph neural network is designed for updating embedding vectors of heterogeneous nodes based on a bidirectional message passing neural network.This framework exploits gated recurrent units and residual blocks to address the gradient disappearance in deep graph recurrent neural networks.Finally,predictions are generated by feeding the embedding vectors into a readout module.Simulation results show that the proposed decoder is more robust than the existing ones in the presence of bursty interference and exhibits high universality.
基金supported by National Natural Science Foundation of China(No.62471054).
文摘The construction of polar codes in corre-lated block fading channels is still an open issue to be solved.In this paper,to explicitly reveal the impact of correlation on error performance of polar coded diver-sity communication systems,an integrated framework has been established to analyze the theoretical error performance of polar codes in correlated block fading channels.First,the upper bound on error probabil-ity of polarized channels is derived based on split po-lar spectrum,which is fully determined by covariance channel matrix as well as the block-wise weight distri-bution of the corresponding polar subcode.Further,to facilitate practical implementations,we design a con-struction metric named polarized correlation weight(PCW)to generate polar codes in correlated block fad-ing channels.Finally,simulation results on block error rate indicate that the proposed metric can exhibit both diversity gain and coding gain compared to the con-ventional methods under successive cancellation de-coding.
基金partially supported by the National Key Research and Development Project under Grant 2020YFB1806805。
文摘Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulting in high decoding complexity and latency.To alleviate this issue,we incorporate the LDPC-CRC-Polar coding scheme with BPBF and propose an improved belief propagation decoder for LDPC-CRC-Polar codes with bit-freezing(LDPCCRC-Polar codes BPBFz).The proposed LDPCCRC-Polar codes BPBFz employs the LDPC code to ensure the reliability of the flipping set,i.e.,critical set(CS),and dynamically update it.The modified CS is further utilized for the identification of error-prone bits.The proposed LDPC-CRC-Polar codes BPBFz obtains remarkable error correction performance and is comparable to that of the CA-SCL(L=16)decoder under medium-to-high signal-to-noise ratio(SNR)regions.It gains up to 1.2dB and 0.9dB at a fixed BLER=10-4compared with BP and BPBF(CS-1),respectively.In addition,the proposed LDPC-CRC-Polar codes BPBFz has lower decoding latency compared with CA-SCL and BPBF,i.e.,it is 15 times faster than CA-SCL(L=16)at high SNR regions.
基金financially supported in part by National Key R&D Program of China(No.2018YFB1801402)in part by Huawei Technologies Co.,Ltd.
文摘In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.
基金funded by the Key Project of NSFC-Guangdong Province Joint Program(Grant No.U2001204)the National Natural Science Foundation of China(Grant Nos.61873290 and 61972431)+1 种基金the Science and Technology Program of Guangzhou,China(Grant No.202002030470)the Funding Project of Featured Major of Guangzhou Xinhua University(2021TZ002).
文摘Belief propagation list(BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL(CA-SCL) decoding.In this work, an improved segmented belief propagation list decoding based on bit flipping(SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the errorcorrection performance of BPL decoding for medium and long codes. It is more than 0.25 d B better than the state-of-the-art BPL decoding at a block error rate(BLER) of 10^(-5), and outperforms CA-SCL decoding in the low signal-to-noise(SNR) region for(1024, 0.5)polar codes.
基金Supported by Headquarters Technology Project of State Grid Corporation of China(No.5700-202118203A-0-0-00)。
文摘Power line communication(PLC)has the potential to become the preferred technique for providing broadband communication to homes and offices with advantage of eliminating the need for new wiring infrastructure and reducing the cost.But it suffers from the impulsive noise because it introduces significant time variance into the power line channel.In this paper,a polar codes based orthogonal frequency division multiplexing(OFDM)PLC system is proposed to deal with the impulsive noise and thereby improve the transmission performance.Firstly,the impulsive noise is modelled with a multi-damped sine function by analyzing the time behavior of impulse events.Then the polar codes are used to combat the impulsive noise of PLC channel,and a low complexity bit-flipping decoding method based on CRC-aided successive cancellation list(CA-SCL)decoding algorithm is proposed.Simulations evaluate the proposed decoding algorithm and the results validate the suggested polar codes based OFDM-PLC scheme which can improve the BER performance of PLC with impulsive interference.
基金supported in part by the Key Program of National Natural Science Foundation of China (No.92067202)in part by the National Natural Science Foundation of China (No.62071058)in part by the Major Key Project of PCL (PCL2021A15)。
文摘After the pursuit of seventy years,the invention of polar codes indicates that we have found the first capacity-achieving coding with low complexity construction and decoding,which is the great breakthrough of the coding theory in the past two decades.In this survey,we retrospect the history of polar codes and summarize the advancement in the past ten years.First,the primary principle of channel polarization is investigated such that the basic construction,coding method and the classic successive cancellation(SC)decoding are reviewed.Second,in order to improve the performance of the finite code length,we introduce the guiding principle and conclude five design criteria for the construction,design and implementation of the polar code in the practical communication system based on the exemplar schemes in the literature.Especially,we explain the design principle behind the concatenated coding and rate matching of polar codes in 5G wireless system.Furthermore,the improved SC decoding algorithms,such as SC list(SCL)decoding and SC stack(SCS)decoding etc.,are investigated and compared.Finally,the research prospects of polar codes for the future 6G communication system are explored,including the optimization of short polar codes,coding construction in fading channels,polar coded modulation and HARQ,and the polar coded transmission,namely polar processing.Predictably,as a new coding methodology,polar codes will shine a light on communication theory and unveil a revolution in transmission technology.
基金jointly supported by the National Nature Science Foundation of China under Grant No.61370040 and 61006018the Fundamental Research Funds for the Central Universities+1 种基金the Priority Academic Program Development of Jiangsu Higher Education InstitutionsOpen Project of State Key Laboratory of ASIC & System(Fudan University)12KF006
文摘Polar codes have become increasingly popular recently because of their capacity achieving property.In this paper,a memory efficient stage-combined belief propagation(BP) decoder design for polar codes is presented.Firstly,we briefly reviewed the conventional BP decoding algorithm.Then a stage-combined BP decoding algorithm which combines two adjacent stages into one stage and the corresponding belief message updating rules are introduced.Based on this stage-combined decoding algorithm,a memory-efficient polar BP decoder is designed.The demonstrated decoder design achieves 50%memory and decoding latency reduction in the cost of some combinational logic complexity overhead.The proposed decoder is synthesized under TSMC 45 nm Low Power CMOS technology.It achieves 0.96 Gb/s throughput with 14.2mm^2 area when code length N=2^(16)which reduces 51.5%decoder area compared with the conventional decoder design.
基金supported in part by the National Key Research and Development Program of China under Grant 2018YFB1802303in part by the Zhejiang Provincial Natural Science Foundation of China under Grant LQ20F010010。
文摘Recently,a generalized successive cancellation list(SCL)decoder implemented with shiftedpruning(SP)scheme,namely the SCL-SP-ωdecoder,is presented for polar codes,which is able to shift the pruning window at mostωtimes during each SCL re-decoding attempt to prevent the correct path from being eliminated.The candidate positions for applying the SP scheme are selected by a shifting metric based on the probability that the elimination occurs.However,the number of exponential/logarithm operations involved in the SCL-SP-ωdecoder grows linearly with the number of information bits and list size,which leads to high computational complexity.In this paper,we present a detailed analysis of the SCL-SP-ωdecoder in terms of the decoding performance and complexity,which unveils that the choice of the shifting metric is essential for improving the decoding performance and reducing the re-decoding attempts simultaneously.Then,we introduce a simplified metric derived from the path metric(PM)domain,and a custom-tailored deep learning(DL)network is further designed to enhance the efficiency of the proposed simplified metric.The proposed metrics are both free of transcendental functions and hence,are more hardware-friendly than the existing metrics.Simulation results show that the proposed DL-aided metric provides the best error correction performance as comparison with the state of the art.
基金Science Foundation of China under Grant No.61871032in part by the Chinese Ministry of Education-China Mobile Communication Corporation Research Fund under Grant MCM20170101+1 种基金the Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant 20KJB510036the Guangxi Key Laboratory of Multimedia Communications and Network Technology under Grant KLF-2020-03。
文摘Non-orthogonal multiple access(NOMA)is deemed to have a superior spectral efficiency and polar codes have became the channel coding scheme for control channel of enhanced mobile broadband(eMBB)in the fifth generation(5G)communication systems.In this paper,NOMA combined with polar codes is used to achieve secure transmission.Both degraded wiretap channel and non-degraded wiretap channel are considered,where an eavesdropper intercepts the communication between base station(BS)and users.For the degraded wiretap channel scenario,a secure polar encoding scheme is proposed in NOMA systems with power allocation to achieve the maximum secrecy capacity.With regard to the nondegraded wiretap channel,a polar encoding scheme with multiple-input-single-output(MISO)system is proposed,where artificial noise is generated at BS to confuse the eavesdropper’s channel via transmit beamforming.The security and the secure rate are employed respectively in order to measure the secrecy performance.We prove that the proposed schemes for each scenario can achieve the secure rate and can transmit the signal securely and reliably.The simulation results show that the eavesdropper hardly decoding the secure signal when the legitimate receiver can decode the signal with very low block error rate(BLER).
基金supported in part by the National Natural Science Foundation of China under Grant 92067202,Grant 62071058.
文摘In this paper,we propose an arbitrary decode-forward single-relay scheme for finite blocklength polar codes,which can be applied to the general symmetric discrete memoryless relay channel with orthogonal receiver components.The relay node decodes the received message.The relay node selectively re-encodes the message and transmits it to the destination node.Furthermore,in order to minimize the upper-bound of the block error probability,we propose a selection strategy to decide the proper re-encoded bit set by the relay.Simulation results are presented to illustrate the improvement in decoding performance of the proposed scheme compared to conventional relay schemes in both additive white Gaussian noise(AWGN)channel and Rayleigh fading channel(RFC).
文摘The increasing data traffic rate of wireless communication systems forces the development of new technologies mandatory.Providing high data rate,extremely low latency and improvement on quality of service are the main subjects of next generation 5G wireless communication systems which will be in the people’s life in the years of 2020.As the newest and first mathematically proven forward error correction code,polar code is one of the best candidates among error correction methods that can be employed for 5G wireless networks.The aim of this tutorial is to show that belief propagation decoding of polar codes can be a promising forward error correction technique in upcoming 5G frameworks.First,we survey the novel approaches to the belief propagation based decoding of polar codes and continue with the studies about the simplification of these decoders.Moreover,early detection and termination methods and concept of scheduling are going to be presented throughout the manuscript.Finally,polar construction algorithms,error types in belief propagation based decoders and hardware implementations are going to be mentioned.Overall,this tutorial proves that the BP based decoding of polar codes has a great potential to be a part of communication standards.
基金supported in part by Joint Fund for Smart Computing of Natural Science Foundation of Shandong Province(ZR2019LZH001)Shandong University Youth Innovation Supporting Program(2019KJN020,2019KJN024)+1 种基金Shandong Key Research and Development Project(2019GGX101066)the Taishan Scholar Program of Shandong Province,the Natural Science Foundation of China(61701284).
文摘To remove the restriction on code length of polar codes,this paper proposes a construction scheme,called stepwise polar codes,which can gen-erate arbitrary-length polar codes.The stepwise polar codes are generated by sub-polar codes with different code lengths.To improve coding performance,sub-polar codes are united by polarization effect priority algorithm,which can reduce the number of in-completely polarized channels.Then,the construction method of the generator matrix of the stepwise po-lar code is presented.Furthermore,we prove that the proposed scheme has lower decoding complexity than punctured,multi-kernel polar codes.Simulation results show that the proposed method can achieve similar decoding performance compared with the conventional punctured polar codes,rate-compatible punctured polar code,PC-short and asymmetric polar codes(APC)when code length N=48 and 72,respectively.
文摘Mission critical Machine-type Communication(mcMTC),also referred to as Ultra-reliable Low Latency Communication(URLLC),has become a research hotspot.It is primarily characterized by communication that provides ultra-high reliability and very low latency to concurrently transmit short commands to a massive number of connected devices.While the reduction in physical(PHY)layer overhead and improvement in channel coding techniques are pivotal in reducing latency and improving reliability,the current wireless standards dedicated to support mcMTC rely heavily on adopting the bottom layers of general-purpose wireless standards and customizing only the upper layers.The mcMTC has a significant technical impact on the design of all layers of the communication protocol stack.In this paper,an innovative bottom-up approach has been proposed for mcMTC applications through PHY layer targeted at improving the transmission reliability by implementing ultra-reliable channel coding scheme in the PHY layer of IEEE 802.11a standard bearing in mind short packet transmission system.To achieve this aim,we analyzed and compared the channel coding performance of convolutional codes(CCs),low-density parity-check(LDPC)codes,and polar codes in wireless network on the condition of short data packet transmission.The Viterbi decoding algorithm(VA),logarithmic belief propagation(Log-BP)algorithm,and cyclic redundancy check(CRC)successive cancellation list(SCL)(CRC-SCL)decoding algorithm were adopted to CC,LDPC codes,and polar codes,respectively.Consequently,a new PHY layer for mcMTC has been proposed.The reliability of the proposed approach has been validated by simulation in terms of Bit error rate(BER)and packet error rate(PER)vs.signal-to-noise ratio(SNR).The simulation results demonstrate that the reliability of IEEE 802.11a standard has been significantly improved to be at PER=10−5 or even better with the implementation of polar codes.The results also show that the general-purpose wireless networks are prominent inproviding short packet mcMTC with the modification needed.
基金This work is partially supported by the National Key Research and Development Project under Grant 2018YFB1802402.
文摘The error correction performance of Belief Propagation(BP)decoding for polar codes is satisfactory compared with the Successive Cancellation(SC)decoding.Nevertheless,it has to complete a fixed number of iterations,which results in high computational complexity.This necessitates an intelligent identification of successful BP decoding for early termination of the decoding process to avoid unnecessary iterations and minimize the computational complexity of BP decoding.This paper proposes a hybrid technique that combines the“paritycheck”with the“G-matrix”to reduce the computational complexity of BP decoder for polar codes.The proposed hybrid technique takes advantage of the parity-check to intelligently identify the valid codeword at an early stage and terminate the BP decoding process,which minimizes the overhead of the G-matrix and reduces the computational complexity of BP decoding.We explore a detailed mechanism incorporating the parity bits as outer code and prove that the proposed hybrid technique minimizes the computational complexity while preserving the BP error correction performance.Moreover,mathematical formulation for the proposed hybrid technique that minimizes the computation cost of the G-matrix is elaborated.The performance of the proposed hybrid technique is validated by comparing it with the state-of-the-art early stopping criteria for BP decoding.Simulation results show that the proposed hybrid technique reduces the iterations by about 90%of BP decoding in a high Signal-to-Noise Ratio(SNR)(i.e.,3.5~4 dB),and approaches the error correction performance of G-matrix and conventional BP decoder for polar codes.
文摘The soft cancellation decoding of polar codes achieves a better performance than the belief propagation decoding with lower computational time and space complexities.However,because the soft cancellation decoding is based on the successive cancellation decoding,the decoding efficiency and performance with finite-length blocks can be further improved.Exploiting the idea of the successive cancellation list decoding,the soft cancellation decoding can be improved in two aspects:one is by adding branch decoding to the error-prone information bits to increase the accuracy of the soft information,and the other is through using partial iterative decoding to reduce the time and computational complexities.Compared with the original method,the improved soft cancellation decoding makes progress in the error correction performance,increasing the decoding efficiency and reducing the computational complexity,at the cost of a small increase of space complexity.
基金supported by the National Natural Science Foundation of China(No.61171099,No.61671080),Nokia Beijing Bell lab
文摘Soft decode-and-forward(DF) can combine the advantages of both amplify-and-forward and hard DF in relay channels. In this paper, we propose a low-complexity soft DF scheme based on polar codes, which features two key techniques: a low-complexity cyclic redundancy check(CRC) aided list successive cancellation(CALSC) decoder and a soft information calculation method. At the relay node, a low-complexity CALSC decoder is designed to reduce the computational complexity by adjusting the list size according to the reliabilities of decoded bits. Based on the path probability metric of the CALSC decoder, we propose a method to compute the soft information of the decoded bits in CALSC. Simulation results show that our proposed scheme outperforms the soft DF based on low-density parity-check codes and the soft DF with belief propagation or soft cancellation decoder, especially in the case when the source-relay channel is at the high signal-to-ratio region.
基金supported by the National Key R&D Program of China(2018YFB2101300)the National Science Foundation of China(61973056)
文摘Polar codes represent one of the major breakthroughs in 5G standard,and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list(SCL)decoding algorithm.However,the SCL algorithm suffers from a large amount of memory overhead.This paper proposes an adaptive simplified decoding algorithm for multiple cyclic redundancy check(CRC)polar codes.Simulation results show that the proposed method can reduce the decoding complexity and memory space.It can also acquire the performance gain in the low signal to noise ratio region.
