In this paper, a novel transmission protocol based on polar coding is proposed for the half-duplex degraded relay channel. In the proposed protocol, referred to as the partial message relaying, the relay only needs to...In this paper, a novel transmission protocol based on polar coding is proposed for the half-duplex degraded relay channel. In the proposed protocol, referred to as the partial message relaying, the relay only needs to forward a part of the decoded source message that the destination needs according to the exquisite nested structure of polar codes. Theoretically, it is proved that the scheme can achieve the capacity of the half-duplex relay channel under the decode-and-forward （DF） cooperation strategy while enjoying low encoding/decoding complexity. Practically, in order to minimize the global transmission power, the optimization of the power allocation is performed between the source and the relay by using information theoretic tools. Furthermore, a joint iterative soft parallel interference cancellation receiver structure is developed to suit to the proposed scheme. Simulation results show that the proposed scheme outperforms the conventional scheme designed by low-density parity-check （LDPC） codes.展开更多
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
Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long bee...Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long been outperformed by CRCaided successive cancellation list(CA-SCL)decoders.To increase the competitiveness of 5G NR LP polar decoding,it is possible to gain performance improvements by exploiting the cyclic redundancy check(CRC)setup.In this paper,we propose a combined scheme of reduced sparsified factor graph-sparsified CRC(RSFG-SCRC)and augmented generator matrix-CRC(AGM-CRC),for polytope generation in adaptive linear programming(ALP)decoder for 5G polar codes.Augmented generator matrix(AGM)polytope and improved maximum cycle strategy-auxiliary node pairs 4(MCS-ANP-4)algorithm are proposed,to make efficient use of CRC constraints and minimize the constraint size for the decoder.Numerical simulations show that adaptive linear programming decoders with our proposed RSFG-SCRC and AGM-CRC polytopes can achieve significantly better block error rate(BLER)performance than a benchmark CA-SCL-8 decoder especially in harsh low-to-medium SNR regions.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
Soft-cancellation(SCAN) is a soft output iterative algorithm widely used in polar decoding. This algorithm has better decoding performance than reduced latency soft-cancellation(RLSC) algorithm, which can effectively ...Soft-cancellation(SCAN) is a soft output iterative algorithm widely used in polar decoding. This algorithm has better decoding performance than reduced latency soft-cancellation(RLSC) algorithm, which can effectively reduce the decoding delay of SCAN algorithm by 50% but has obvious performance loss. A modified reduced latency soft-cancellation(MRLSC) algorithm is presented in the paper. Compared with RLSC algorithm, LLR information storage required in MRLSC algorithm can be reduced by about 50%, and better decoding performance can be achieved with only a small increase in decoding delay. The simulation results show that MRLSC algorithm can achieve a maximum block error rate(BLER) performance gain of about 0.4 dB compared with RLSC algorithm when code length is 2048. At the same time, compared with the performance of several other algorithms under(1024, 512) polar codes, the results show that the throughput of proposed MRLSC algorithm has the advantage at the low and medium signal-to-noise ratio(SNR) and better BLER performance at the high SNR.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
This paper considers the use of polar codes to enable secure transmission over parallel relay channels.By exploiting the properties of polar codes over parallel channels, a polar encoding algorithm is designed based o...This paper considers the use of polar codes to enable secure transmission over parallel relay channels.By exploiting the properties of polar codes over parallel channels, a polar encoding algorithm is designed based on Channel State Information（CSI） between the legitimate transmitter（Alice） and the legitimate receiver（Bob）.Different from existing secure transmission schemes, the proposed scheme does not require CSI between Alice and the eavesdropper（Eve）. The proposed scheme is proven to be reliable and shown to be capable of transmitting information securely under Amplify-and-Forward（AF） relay protocol, thereby providing security against passive and active attackers.展开更多
Binary Polar Codes (BPCs) have advantages of high-efficiency and capacity-achieving but suffer from large latency due to the Successive-Cancellation List (SCL) decoding. Non-Binary Polar Codes (NBPCs) have been invest...Binary Polar Codes (BPCs) have advantages of high-efficiency and capacity-achieving but suffer from large latency due to the Successive-Cancellation List (SCL) decoding. Non-Binary Polar Codes (NBPCs) have been investigated to obtain the performance gains and reduce latency under the implementation of parallel architectures for multi-bit decoding. However, most of the existing works only focus on the Reed-Solomon matrix-based NBPCs and the probability domain-based non-binary polar decoding, which lack flexible structure and have a large computation amount in the decoding process, while little attention has been paid to general non-binary kernel-based NBPCs and Log-Likelihood Ratio (LLR) based decoding methods. In this paper, we consider a scheme of NBPCs with a general structure over GF(2m). Specifically, we pursue a detailed Monte-Carlo simulation implementation to determine the construction for proposed NBPCs. For non-binary polar decoding, an SCL decoding based on LLRs is proposed for NBPCs, which can be implemented with non-binary kernels of arbitrary size. Moreover, we propose a Perfect Polarization-Based SCL (PPB-SCL) algorithm based on LLRs to reduce decoding complexity by deriving a new update function of path metric for NBPCs and eliminating the path splitting process at perfect polarized (i.e., highly reliable) positions. Simulation results show that the bit error rate of the proposed NBPCs significantly outperforms that of BPCs. In addition, the proposed PPB-SCL decoding obtains about a 40% complexity reduction of SCL decoding for NBPCs.展开更多
In this paper,we propose a new class of nonbinary polar codes,where the symbol-level polarization is achieved by using a 2×2 q-ary matrix[10β1]as the kernel.Under bit-level code construction,some partially-froze...In this paper,we propose a new class of nonbinary polar codes,where the symbol-level polarization is achieved by using a 2×2 q-ary matrix[10β1]as the kernel.Under bit-level code construction,some partially-frozen symbols exist,where the frozen bits in these symbols can be used as activecheck bits to facilitate the decoder.The encoder/decoder of the proposed codes has a similar structure to the original binary polar codes,admitting an easily configurable and flexible implementation,which is an obvious advantage over the existing nonbinary polar codes based on ReedSolomon(RS)codes.A low-complexity decoding method is also introduced,in which only more competitive symbols are considered rather than the whole q symbols in the finite field.To support high spectral efficiency,we also present,in addition to the single level coded modulation scheme with field-matched modulation order,a mixed multilevel coded modulation scheme with arbitrary modulation in order to trade off the latency against complexity.Simulation results show that our proposed nonbinary polar codes exhibit comparable performance with the RS4-based polar codes and outperform binary polar codes with low decoding latency,suggesting a potential application for future ultra-reliable and low-latency communications(URLLC).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
Belief propagation(BP)decoding outputs soft information and can be naturally used in iterative receivers.BP list(BPL)decoding provides comparable error-correction performance to the successive cancellation list(SCL)de...Belief propagation(BP)decoding outputs soft information and can be naturally used in iterative receivers.BP list(BPL)decoding provides comparable error-correction performance to the successive cancellation list(SCL)decoding.In this paper,we firstly introduce an enhanced code construction scheme for BPL decoding to improve its errorcorrection capability.Then,a GPU-based BPL decoder with adoption of the new code construction is presented.Finally,the proposed BPL decoder is tested on NVIDIA RTX3070 and GTX1060.Experimental results show that the presented BPL decoder with early termination criterion achieves above 1 Gbps throughput on RTX3070 for the code(1024,512)with 32 lists under good channel conditions.展开更多
This paper introduces bit-interleaved polar coded modulation with iterative detection/decoding(BIPCM-ID).In order to enable the soft output of successive cancellation list(SCL)decoding,two types of re-encoders are pro...This paper introduces bit-interleaved polar coded modulation with iterative detection/decoding(BIPCM-ID).In order to enable the soft output of successive cancellation list(SCL)decoding,two types of re-encoders are proposed,namely the max-re-encoder and min-re-encoder,respectively.Regarding the iterative decoding,we analytically verify that the average mutual information(AMI)between the transmitted and decoded symbols can approach the Shannon bound with the proposed schemes.Moreover,bit error rate(BER)and block error rate(BLER)in single-user and multi-user scenarios are studied.Finally,simulation results show that the performance of BIPCMID outperforms other bit-interleaved coded modulation(BICM)systems with LDPC and Turbo codes,while also reducing the computational complexity.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
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
<div style="text-align:justify;"> Polar codes using successive-cancellation decoding always suffer from high latency for its serial nature. Fast simplified successive-cancellation decoding algorithm im...<div style="text-align:justify;"> Polar codes using successive-cancellation decoding always suffer from high latency for its serial nature. Fast simplified successive-cancellation decoding algorithm improves the situation in theoretically but not performs well as expected in practical for the workload of nodes identification and the existence of many short blocks. Meanwhile, Neural network (NN) based decoders have appeared as potential candidates to replace conventional decoders for polar codes. But the exponentially increasing training complexity with information bits is unacceptable which means it is only suitable for short codes. In this paper, we present an improvement that increases decoding efficiency without degrading the error-correction performance. The long polar codes are divided into several sub-blocks, some of which can be decoded adopting fast maximum likelihood decoding method and the remained parts are replaced by several short codes NN decoders. The result shows that time steps the proposed algorithm need only equal to 79.8% of fast simplified successive-cancellation decoders require. Moreover, it has up to 21.2 times faster than successive-cancellation decoding algorithm. More importantly, the proposed algorithm decreases the hardness when applying in some degree. </div>展开更多
<div style="text-align:justify;"> <p style="text-align:justify;background:white;"> <span style="font-size:10.0pt;font-family:" color:black;"="">This artic...<div style="text-align:justify;"> <p style="text-align:justify;background:white;"> <span style="font-size:10.0pt;font-family:" color:black;"="">This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's </span><span><a href="http://publicationethics.org/files/retraction%20guidelines.pdf"><span style="font-size:10.0pt;font-family:;" "="">Retraction Guidelines</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"="">. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.</span><span style="font-size:10.0pt;font-family:" color:black;"=""></span> </p> <p style="text-align:justify;background:white;"> <span style="font-size:10.0pt;font-family:" color:black;"="">Please see the </span><span><a href="https://www.scirp.org/journal/paperinformation.aspx?paperid=101825"><span style="font-size:10.0pt;font-family:;" "="">article page</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"=""> for more details. </span><span><a href="https://www.scirp.org/pdf/opj_2020072814494052.pdf"><span style="font-size:10.0pt;font-family:;" "="">The full retraction notice</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"=""> in PDF is preceding the original paper which is marked "RETRACTED". </span> </p> <br /> </div>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
The syndrome a posteriori probability of the log-likelihood ratio of intercepted codewords is used to develop an algorithm that recognizes the polar code length and generator matrix of the underlying polar code.Based ...The syndrome a posteriori probability of the log-likelihood ratio of intercepted codewords is used to develop an algorithm that recognizes the polar code length and generator matrix of the underlying polar code.Based on the encoding structure,three theorems are proved,two related to the relationship between the length and rate of the polar code,and one related to the relationship between frozen-bit positions,information-bit positions,and codewords.With these three theorems,polar codes can be quickly reconstruced.In addition,to detect the dual vectors of codewords,the statistical characteristics of the log-likelihood ratio are analyzed,and then the information-and frozen-bit positions are distinguished based on the minimumerror decision criterion.The bit rate is obtained.The correctness of the theorems and effectiveness of the proposed algorithm are validated through simulations.The proposed algorithm exhibits robustness to noise and a reasonable computational complexity.展开更多
In 5G new radio(NR), polar codes are adopted for e MBB downlink control channels where the blind detection is employed in user equipment(UE) to identify the correct downlink control information(DCI). However, differen...In 5G new radio(NR), polar codes are adopted for e MBB downlink control channels where the blind detection is employed in user equipment(UE) to identify the correct downlink control information(DCI). However, different from that in the 4G LTE system, the cyclic redundancy check(CRC) in polar decoding plays both error correction and error detection roles. Consequently, the false alarm rates(FAR) may not meet the system requirements(FAR<1.52 × 10^(−5)). In this paper, to mitigate the FAR in polar code blind detection, we attach a binary classifier after the polar decoder to further remove the false alarm results and meanwhile retain the correct DCI. This classifier works by tracking the squared Euclidean distance ratio(SEDR) between the received signal and hypothesis. We derive an analytical method to fast compute proper classification threshold that is implementation-friendly in practical use. Combining the well-designed classifier, we show that some very short CRC sequences can even be used to meet the FAR requirements. This consequently reduces the CRC overhead and contributes to the system error performance improvements.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
文摘In this paper, a novel transmission protocol based on polar coding is proposed for the half-duplex degraded relay channel. In the proposed protocol, referred to as the partial message relaying, the relay only needs to forward a part of the decoded source message that the destination needs according to the exquisite nested structure of polar codes. Theoretically, it is proved that the scheme can achieve the capacity of the half-duplex relay channel under the decode-and-forward （DF） cooperation strategy while enjoying low encoding/decoding complexity. Practically, in order to minimize the global transmission power, the optimization of the power allocation is performed between the source and the relay by using information theoretic tools. Furthermore, a joint iterative soft parallel interference cancellation receiver structure is developed to suit to the proposed scheme. Simulation results show that the proposed scheme outperforms the conventional scheme designed by low-density parity-check （LDPC） codes.
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 China Postdoctoral Science Foundation(No.2020M670469)National Key Research and Development Program of China(No.2019YFB1803303,No.2020YFB1806702).
文摘Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long been outperformed by CRCaided successive cancellation list(CA-SCL)decoders.To increase the competitiveness of 5G NR LP polar decoding,it is possible to gain performance improvements by exploiting the cyclic redundancy check(CRC)setup.In this paper,we propose a combined scheme of reduced sparsified factor graph-sparsified CRC(RSFG-SCRC)and augmented generator matrix-CRC(AGM-CRC),for polytope generation in adaptive linear programming(ALP)decoder for 5G polar codes.Augmented generator matrix(AGM)polytope and improved maximum cycle strategy-auxiliary node pairs 4(MCS-ANP-4)algorithm are proposed,to make efficient use of CRC constraints and minimize the constraint size for the decoder.Numerical simulations show that adaptive linear programming decoders with our proposed RSFG-SCRC and AGM-CRC polytopes can achieve significantly better block error rate(BLER)performance than a benchmark CA-SCL-8 decoder especially in harsh low-to-medium SNR regions.
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.
基金the Zhejiang Provincial Natural Science Foundation of China under Grant No. Y20F010069supported in part by the National Natural Science Foundation of China (NSFC) under Grant No. 51874264, 61571108Key Laboratory of Electromagnetic Wave Information Technology and Metrology of Zhejiang Province, College of Information Engineering, China Jiliang University, Hangzhou 310018, China
文摘Soft-cancellation(SCAN) is a soft output iterative algorithm widely used in polar decoding. This algorithm has better decoding performance than reduced latency soft-cancellation(RLSC) algorithm, which can effectively reduce the decoding delay of SCAN algorithm by 50% but has obvious performance loss. A modified reduced latency soft-cancellation(MRLSC) algorithm is presented in the paper. Compared with RLSC algorithm, LLR information storage required in MRLSC algorithm can be reduced by about 50%, and better decoding performance can be achieved with only a small increase in decoding delay. The simulation results show that MRLSC algorithm can achieve a maximum block error rate(BLER) performance gain of about 0.4 dB compared with RLSC algorithm when code length is 2048. At the same time, compared with the performance of several other algorithms under(1024, 512) polar codes, the results show that the throughput of proposed MRLSC algorithm has the advantage at the low and medium signal-to-noise ratio(SNR) and better BLER performance at the high SNR.
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supported in part by the National Natural Science Foundation of China(No.61371075)Beijing Municipal Science and Technology Project(No.D171100006317001)
文摘This paper considers the use of polar codes to enable secure transmission over parallel relay channels.By exploiting the properties of polar codes over parallel channels, a polar encoding algorithm is designed based on Channel State Information（CSI） between the legitimate transmitter（Alice） and the legitimate receiver（Bob）.Different from existing secure transmission schemes, the proposed scheme does not require CSI between Alice and the eavesdropper（Eve）. The proposed scheme is proven to be reliable and shown to be capable of transmitting information securely under Amplify-and-Forward（AF） relay protocol, thereby providing security against passive and active attackers.
基金supported in part by the National Natural Science Foundation of China under Grant 61401407in part by the Fundamental Research Funds for the Central Universities under Grant CUC2019B067.
文摘Binary Polar Codes (BPCs) have advantages of high-efficiency and capacity-achieving but suffer from large latency due to the Successive-Cancellation List (SCL) decoding. Non-Binary Polar Codes (NBPCs) have been investigated to obtain the performance gains and reduce latency under the implementation of parallel architectures for multi-bit decoding. However, most of the existing works only focus on the Reed-Solomon matrix-based NBPCs and the probability domain-based non-binary polar decoding, which lack flexible structure and have a large computation amount in the decoding process, while little attention has been paid to general non-binary kernel-based NBPCs and Log-Likelihood Ratio (LLR) based decoding methods. In this paper, we consider a scheme of NBPCs with a general structure over GF(2m). Specifically, we pursue a detailed Monte-Carlo simulation implementation to determine the construction for proposed NBPCs. For non-binary polar decoding, an SCL decoding based on LLRs is proposed for NBPCs, which can be implemented with non-binary kernels of arbitrary size. Moreover, we propose a Perfect Polarization-Based SCL (PPB-SCL) algorithm based on LLRs to reduce decoding complexity by deriving a new update function of path metric for NBPCs and eliminating the path splitting process at perfect polarized (i.e., highly reliable) positions. Simulation results show that the bit error rate of the proposed NBPCs significantly outperforms that of BPCs. In addition, the proposed PPB-SCL decoding obtains about a 40% complexity reduction of SCL decoding for NBPCs.
基金supported in part by the National Key R&D Program of China(2021YFA1000500)by the National Natural Science Foundation of China(62171356).
文摘In this paper,we propose a new class of nonbinary polar codes,where the symbol-level polarization is achieved by using a 2×2 q-ary matrix[10β1]as the kernel.Under bit-level code construction,some partially-frozen symbols exist,where the frozen bits in these symbols can be used as activecheck bits to facilitate the decoder.The encoder/decoder of the proposed codes has a similar structure to the original binary polar codes,admitting an easily configurable and flexible implementation,which is an obvious advantage over the existing nonbinary polar codes based on ReedSolomon(RS)codes.A low-complexity decoding method is also introduced,in which only more competitive symbols are considered rather than the whole q symbols in the finite field.To support high spectral efficiency,we also present,in addition to the single level coded modulation scheme with field-matched modulation order,a mixed multilevel coded modulation scheme with arbitrary modulation in order to trade off the latency against complexity.Simulation results show that our proposed nonbinary polar codes exhibit comparable performance with the RS4-based polar codes and outperform binary polar codes with low decoding latency,suggesting a potential application for future ultra-reliable and low-latency communications(URLLC).
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 by the Fundamental Research Funds for the Central Universities (FRF-TP20-062A1)Guangdong Basic and Applied Basic Research Foundation (2021A1515110070)
文摘Belief propagation(BP)decoding outputs soft information and can be naturally used in iterative receivers.BP list(BPL)decoding provides comparable error-correction performance to the successive cancellation list(SCL)decoding.In this paper,we firstly introduce an enhanced code construction scheme for BPL decoding to improve its errorcorrection capability.Then,a GPU-based BPL decoder with adoption of the new code construction is presented.Finally,the proposed BPL decoder is tested on NVIDIA RTX3070 and GTX1060.Experimental results show that the presented BPL decoder with early termination criterion achieves above 1 Gbps throughput on RTX3070 for the code(1024,512)with 32 lists under good channel conditions.
文摘This paper introduces bit-interleaved polar coded modulation with iterative detection/decoding(BIPCM-ID).In order to enable the soft output of successive cancellation list(SCL)decoding,two types of re-encoders are proposed,namely the max-re-encoder and min-re-encoder,respectively.Regarding the iterative decoding,we analytically verify that the average mutual information(AMI)between the transmitted and decoded symbols can approach the Shannon bound with the proposed schemes.Moreover,bit error rate(BER)and block error rate(BLER)in single-user and multi-user scenarios are studied.Finally,simulation results show that the performance of BIPCMID outperforms other bit-interleaved coded modulation(BICM)systems with LDPC and Turbo codes,while also reducing the computational complexity.
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.
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.
文摘<div style="text-align:justify;"> Polar codes using successive-cancellation decoding always suffer from high latency for its serial nature. Fast simplified successive-cancellation decoding algorithm improves the situation in theoretically but not performs well as expected in practical for the workload of nodes identification and the existence of many short blocks. Meanwhile, Neural network (NN) based decoders have appeared as potential candidates to replace conventional decoders for polar codes. But the exponentially increasing training complexity with information bits is unacceptable which means it is only suitable for short codes. In this paper, we present an improvement that increases decoding efficiency without degrading the error-correction performance. The long polar codes are divided into several sub-blocks, some of which can be decoded adopting fast maximum likelihood decoding method and the remained parts are replaced by several short codes NN decoders. The result shows that time steps the proposed algorithm need only equal to 79.8% of fast simplified successive-cancellation decoders require. Moreover, it has up to 21.2 times faster than successive-cancellation decoding algorithm. More importantly, the proposed algorithm decreases the hardness when applying in some degree. </div>
文摘<div style="text-align:justify;"> <p style="text-align:justify;background:white;"> <span style="font-size:10.0pt;font-family:" color:black;"="">This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's </span><span><a href="http://publicationethics.org/files/retraction%20guidelines.pdf"><span style="font-size:10.0pt;font-family:;" "="">Retraction Guidelines</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"="">. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.</span><span style="font-size:10.0pt;font-family:" color:black;"=""></span> </p> <p style="text-align:justify;background:white;"> <span style="font-size:10.0pt;font-family:" color:black;"="">Please see the </span><span><a href="https://www.scirp.org/journal/paperinformation.aspx?paperid=101825"><span style="font-size:10.0pt;font-family:;" "="">article page</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"=""> for more details. </span><span><a href="https://www.scirp.org/pdf/opj_2020072814494052.pdf"><span style="font-size:10.0pt;font-family:;" "="">The full retraction notice</span></a></span><span style="font-size:10.0pt;font-family:" color:black;"=""> in PDF is preceding the original paper which is marked "RETRACTED". </span> </p> <br /> </div>
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.
基金supported by the National Natural Science Foundation of China(62371465)Taishan Scholar Project of Shandong Province(ts201511020)the Chinese National Key Laboratory of Science and Technology on Information System Security(6142111190404).
文摘The syndrome a posteriori probability of the log-likelihood ratio of intercepted codewords is used to develop an algorithm that recognizes the polar code length and generator matrix of the underlying polar code.Based on the encoding structure,three theorems are proved,two related to the relationship between the length and rate of the polar code,and one related to the relationship between frozen-bit positions,information-bit positions,and codewords.With these three theorems,polar codes can be quickly reconstruced.In addition,to detect the dual vectors of codewords,the statistical characteristics of the log-likelihood ratio are analyzed,and then the information-and frozen-bit positions are distinguished based on the minimumerror decision criterion.The bit rate is obtained.The correctness of the theorems and effectiveness of the proposed algorithm are validated through simulations.The proposed algorithm exhibits robustness to noise and a reasonable computational complexity.
基金supported in part by National Natural Science Foundation of China(No.62471054)in part by National Natural Science Foundation of China(No.92467301)+3 种基金in part by the National Natural Science Foundation of China(No.62201562)in part by the National Natural Science Foundation of China(No.62371063)in part by the National Natural Science Foundation of China(No.62321001)in part by Liaoning Provincial Natural Science Foundation of China(No.2024–BSBA–51).
文摘In 5G new radio(NR), polar codes are adopted for e MBB downlink control channels where the blind detection is employed in user equipment(UE) to identify the correct downlink control information(DCI). However, different from that in the 4G LTE system, the cyclic redundancy check(CRC) in polar decoding plays both error correction and error detection roles. Consequently, the false alarm rates(FAR) may not meet the system requirements(FAR<1.52 × 10^(−5)). In this paper, to mitigate the FAR in polar code blind detection, we attach a binary classifier after the polar decoder to further remove the false alarm results and meanwhile retain the correct DCI. This classifier works by tracking the squared Euclidean distance ratio(SEDR) between the received signal and hypothesis. We derive an analytical method to fast compute proper classification threshold that is implementation-friendly in practical use. Combining the well-designed classifier, we show that some very short CRC sequences can even be used to meet the FAR requirements. This consequently reduces the CRC overhead and contributes to the system error performance improvements.
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.
