Improved Belief Propagation Decoder for LDPC-CRC-Polar Codes with Bit-Freezing

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.

Quantized Decoders that Maximize Mutual Information for Polar Codes

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.

Improved Segmented Belief Propagation List Decoding for Polar Codes with Bit-Flipping

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.

Physical Layer Encryption of OFDM-PON Based on Quantum Noise Stream Cipher with Polar Code

Orthogonal frequency division multiplexing passive optical network(OFDM-PON) has superior anti-dispersion property to operate in the C-band of fiber for increased optical power budget. However,the downlink broadcast exposes the physical layer vulnerable to the threat of illegal eavesdropping. Quantum noise stream cipher(QNSC) is a classic physical layer encryption method and well compatible with the OFDM-PON. Meanwhile, it is indispensable to exploit forward error correction(FEC) to control errors in data transmission. However, when QNSC and FEC are jointly coded, the redundant information becomes heavier and thus the code rate of the transmitted signal will be largely reduced. In this work, we propose a physical layer encryption scheme based on polar-code-assisted QNSC. In order to improve the code rate and security of the transmitted signal, we exploit chaotic sequences to yield the redundant bits and utilize the redundant information of the polar code to generate the higher-order encrypted signal in the QNSC scheme with the operation of the interleaver.We experimentally demonstrate the encrypted 16/64-QAM, 16/256-QAM, 16/1024-QAM, 16/4096-QAM QNSC signals transmitted over 30-km standard single mode fiber. For the transmitted 16/4096-QAM QNSC signal, compared with the conventional QNSC method, the proposed method increases the code rate from 0.1 to 0.32 with enhanced security.

Polar codes based OFDM-PLC systems in the presence of impulsive noise

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.

A Golden Decade of Polar Codes:From Basic Principle to 5G Applications

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.

Deep Learning Aided SCL Decoding of Polar Codes with Shifted-Pruning

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.

Belief Propagation List Decoding for Polar Codes:Performance Analysis and Software Implementation on GPU

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.

A Construction Method of Arbitrary-Length Polar Codes

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.

Parity-check and G-matrix based intelligent early stopping criterion for belief propagation decoder for polar codes

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.

Arbitrary Decode-Forward Relaying with Re-Encoded Bits Selection Strategy for Polar Codes

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).

A simplified decoding algorithm for multi-CRC polar codes

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.

Secure Transmission in Downlink Non-Orthogonal Multiple Access Based on Polar Codes

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).

Research on encoding and decoding of non-binary polar codes over GF(2m)

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.

Polar Codes多比特同时判定高输出SC算法研究

polar codes具有丰富的代数结构和优秀的分析特性,具有明确的编码方法和译码算法,但是其连续删除译码算法由于采用串行按位译码的方法,从而导致整体译码时间较长。利用改进的路径度量值计算方法减少了SC译码器判定的次数,从而使得整体的译码时间大大降低,提高了原SC算法测输出。实验数据表明该方法不仅拥有较低的译码时间,同时还能获得更好的性能。

Bit-Interleaved Polar Coded Modulation with Iterative Successive Cancellation List Decoding

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.

Deployment of Polar Codes for Mission-Critical Machine-Type Communication Over Wireless Networks

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.

A Survey on Belief Propagation Decoding of Polar Codes

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.

Improved Soft Cancellation Decoding of Polar Codes

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.

Evaluation of the Polar Code in different environments and for different maritime activities in the two polar regions

Because of the decrease in sea ice coverage,maritime activities in the polar regions have increased steadily over the years and several issues related to maritime activities have arisen.It is essential to understand these challenges because they could have serious political,environmental,and economic consequences.Although there are significant geographical and legal differences and differences in the types of activities between the Arctic and the Antarctic,a single International Maritime Organization Polar Code covers both regions.In this analysis,changes in polar regions are introduced,and the differences between the Arctic and Antarctic are discussed.The differences in maritime activities in the two polar regions are then discussed,and the Polar Code is evaluated in terms of these differences.