Successive Cancellation List Decoding Research Articles

Secure RoF system based on key nested polar code and feedback neural network.

With the development of 6 G network, the issue of information security is becoming more and more significant. In this paper, a secure RoF system based on key nested polar code and feedback neural network (FNN) is proposed. For the nested polar code, the original key is randomly selected from the constructed codebook and the index of key is encoded by inner polar code which is placed at the location with better channel quality bit of the frozen bit of outer polar code, for the other part of outer polar code, information bits are encrypted by chaotic sequence generated by 4-D cellular neural network. The polar coded sequence is mapped to the 16-QAM symbol for orthogonal frequency division multiplexing (OFDM) and then the OFDM signal is modulated to the optical pulse, which is delivered to users through 50 km standard single-mode fiber and 5 m wireless channel. In the receiver, successive cancellation list (SCL) decoder is used for decoding outer polar code and FNN is used for decoding inner polar code to reduce the latency. The experimental results show that, compared with the existing scheme, when the bit err rate is 10-3, the received optical power (ROP) gain of the proposed scheme with SCL2 decoder and SCL4 decoder is ∼1.2 dB and ∼1.6 dB, respectively. And compared with the traditional OFDM signal with polar code, when the bit err rate is 10-3, the ROP gain of the proposed scheme with SCL4 decoder is ∼1 dB. What's more, the randomness of the chaotic key sequence, the ability to resist brute-force attacks and the ability to resist chosen-plaintext attacks are elaborated. Therefore, the proposed scheme can greatly improve the security of the system while ensuring the correct transmission of information.

Cyclic redundancy check-aided successive cancellation-based polar decoders

<span>Research on channel coding for network transmission using polar codes has produced excellent results. By removing error redundancy from the decoding process, cyclic redundancy check (CRC) is frequently used by researchers to increase a system’s performance. In prior research, the application of decoder algorithms for polar codes was examined but not thoroughly compared. For the general capabilities of the previously proposed algorithms to be ascertained, it is crucial to analyze the employment of polar decoders especially successive cancellation (SC)-based polar decoders and the use of CRC in additive white gaussian noise (AWGN). Hence, this paper analyzes the performance of CRC with SC-based polar decoders in AWGN. In the simulation setup, (256,128) polar codes and CRCs with three-bit sizes (6, 8 and 11) were utilized. SC-based polar decoders, such as SC, soft-output cancellation, SC list (SCL) and simplified SC, were applied at the decoder part. The outcomes show that CRC-aided SC-based polar decoders reduced redundancy error. Among all the decoders, the SCL decoder with 11-bits CRC performed well when the normalized signal-to-noise ratio was high. Based on the analysis, removing errors at the highest level is possible using a suitable CRC size for SC-based polar decoders.</span>

Scalable Polar Code Construction for Successive Cancellation List Decoding: A Graph Neural Network-Based Approach

Scalable Polar Code Construction for Successive Cancellation List Decoding: A Graph Neural Network-Based Approach

A Note on the Mixing Factor of Polar Codes.

Over binary-input memoryless symmetric (BMS) channels, the performance of polar codes under successive cancellation list (SCL) decoding can approach maximum likelihood (ML) algorithm when the list size L is greater than or equal to 2MF, where MF, known as mixing factor of code, represents the number of information bits before the last frozen bit. Recently, Yao et al. showed the upper bound of the mixing factor of decreasing monomial codes with length n=2m and rate R≤12 when m is an odd number; moreover, this bound is reachable. Herein, we obtain an achievable upper bound in the case of an even number. Further, we propose a new decoding hard-decision rule beyond the last frozen bit of polar codes under BMS channels.

An Improved Bit-Flipping Algorithm of Successive Cancellation List Decoding for Polar Codes

Polar codes, as the coding scheme for the control channel in fifth-generation mobile communication technology (5G), have attracted widespread attention since their proposal. As a mainstream decoding algorithm for polar codes, the successive cancellation list (SCL) decoder usually improves the error correction performance by increasing the list size, but this method suffers from the problems of high decoding complexity. To address this problem, this paper proposes a layered-search bit-flipping (LS-SCLF) decoding algorithm based on SCL decoding. Firstly, a new flip-bit metric is proposed, which derives a formula to approximate the probability of an error occurring in an information bit. This formula introduces a perturbation parameter to improve the calculation accuracy. Secondly, a compromise scheme for determining the perturbation parameter is proposed. The scheme uses Monte Carlo simulation to determine an optimized parameter for the precise positioning of the first erroneous decoded bit under different decoding conditions. Finally, a layered search strategy is adopted to sequentially search the erroneous decoded bits from the low order to high order, which can correct up to multiple bits at the same time. Simulation results show that the proposed algorithm achieves improved error correction performance with a slight increase in decoding complexity compared to the generalized SCL-Flip (GSCLF) decoding algorithm. This algorithm also achieves a good balance between the error correction performance and decoding complexity.

Construction of Polar Codes Based on Memetic Algorithm

As an emerging coding technique chosen by the 5th generation wireless systems (5G) standardization process, polar coding has attracted the attention of both academia and industry in recent years. The currently used construction methods of polar code are generally based on the reliability of each polarized sub-channel, which directly correspond to the Successive Cancellation (SC) decoding algorithm. However, much less is known about the optimal construction of polar codes under more sophisticated decoding methods such as the Successive Cancellation List (SCL) decoding. There is currently no perfect theory to derive the optimal construction for the SCL decoding to the best of our knowledge, because finding such optimal construction of SCL is considered to be a hard problem for normal choices of the list size. To address this problem, in this paper we turn to evolutionary computation, and propose a memetic algorithm by incorporating prior knowledge obtained from both the channel estimation of the SC-profile and the codeword weight evaluation of the RM-profile, shorted as MA-SCRM. The potential constructions of polar codes are expressed as binary sequences which are processed as the individuals of the population in MA-SCRM. Based on the prior knowledge obtained from the SC-profile and the Reed-Muller-profile, we design special initialization and evolutional operators for polar codes construction. An elitism archive is also introduced to maintain promising constructions and accelerate the convergence of the algorithm. For the SCL decoding, MA-SCRM obtains polar-coding constructions that are more excellent than the SC decoder construction in the sense of block error probability. Compared with the SC decoding construction method, MA-SCRM can reduce the block error probability by up to 48.78% for the original block error rate around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-2}$</tex-math></inline-formula> , and more improvement can be observed for lower original block error rate.

Efficient protection of polar decoders against Single Event Upsets (SEUs) on user memories

Polar codes are used in 5G systems for the transmission of control channels due to their excellent error correction capability for short sequences. CRC aided successive cancellation list (CA-SCL) decoders are commonly used in practical systems. When used in critical environments, e.g. space platforms, memories used in the polar decoder will suffer single-event upsets (SEUs) that can cause failures and disrupt communications. Therefore, the protection of polar decoders against SEUs on memories with low overhead is an important problem, especially for resource-limited on-board space systems. In this paper, efficient protection schemes are first proposed for each of the main memory components of CA-SAL decoders based on their algorithmic properties. Then FPGA implementation and hardware-based fault injection experiments are performed to evaluate the protection overhead and reliability of the proposed schemes. Experimental results show that, relative to the unprotected decoder, the reliability of the decoder is improved by more than two orders of magnitude, and the overhead of memory and computation are only about 1.26 and 1.23 times of those of unprotected decoder.

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 error-correction 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.

Fully parallel low‐density parity‐check code‐based polar decoder architecture for 5G wireless communications

AbstractA hardware architecture is presented to decode (N, K) polar codes based on a low‐density parity‐check code‐like decoding method. By applying suitable pruning techniques to the dense graph of the polar code, the decoder architectures are optimized using fewer check nodes (CN) and variable nodes (VN). Pipelining is introduced in the CN and VN architectures, reducing the critical path delay. Latency is reduced further by a fully parallelized, single‐stage architecture compared with the log N stages in the conventional belief propagation (BP) decoder. The designed decoder for short‐to‐intermediate code lengths was implemented using the Virtex‐7 field‐programmable gate array (FPGA). It achieved a throughput of 2.44 Gbps, which is four times and 1.4 times higher than those of the fast‐simplified successive cancellation and combinational decoders, respectively. The proposed decoder for the (1024, 512) polar code yielded a negligible bit error rate of 10−4 at 2.7 Eb/No (dB). It converged faster than the BP decoding scheme on a dense parity‐check matrix. Moreover, the proposed decoder is also implemented using the Xilinx ultra‐scale FPGA and verified with the fifth generation new radio physical downlink control channel specification. The superior error‐correcting performance and better hardware efficiency makes our decoder a suitable alternative to the successive cancellation list decoders used in 5G wireless communication.

Neural Network Aided Path Splitting Strategy for Polar Successive Cancellation List Decoding

Combined with the path splitting selecting (PSS) strategy, the successive cancellation list (SCL) decoder achieves a lower decoding complexity without any performance loss. The main purpose of the PSS strategy is to select fewer non-frozen bits to perform the path splitting and pruning operations. To make the selection more efficient, a neural network aided path splitting selecting strategy is proposed in this paper. In the proposed method, the path splitting is seen as a classification problem. With the help of the neural network, the proposed method can precisely locate the non-frozen bits which are needed to be split. Simulation results verify that the proposed method can reduce the sorting complexity (which is equal to the number of path splitting) without any performance loss.

Low-Rate and Short-Block-Length Random Permutation-Coded Modulations Achieve Finite-Length Bounds

Ultra-reliable low-latency communication (URLLC) is an important feature brought by 5G New Radio (NR). By using a block code, the low-latency requirement in general requires a short block length in order to reduce the latency of transmitting the entire code block. The ultra-reliable communication requires a low-rate code to achieve high decoding reliability even under low signal-to-noise ratios (SNRs). This paper proposes a new class of coding and modulation schemes, termed permutation-coded modulations, for low-rate and short-block-length applications, such as URLLC. We show that permutation-coded modulations under maximum-likelihood (ML) decoding have remarkable performance levels that achieve the dispersion bounds with normal approximation (NA) for short block lengths. However, their encoding and ML-decoding complexities are prohibitive if the number of message bits transmitted per code block increases. To reduce the encoding and decoding complexities, we propose a trapezoidal permutation-coded modulation scheme which can be decoded efficiently by successive cancellation list (SCL) decoders. We also show that the trapezoidal permutation-coded modulations under SCL decoding can achieve the dispersion bounds with NA for short block lengths.

Decoding of the extended Golay code by the simplified successive-cancellation list decoder adapted to multi-kernel polar codes

This paper describes an adaptation of a polar code decoding technique in favor of the extended Golay code. Based on the bridge provided by a permutation matrix between the code words of these two classes of codes, the Golay code can be decoded by any polar code technique. Contrary to the successive-cancellation list technique which is characterized by a serial estimation of the bits, we propose in this work an adaptation of the simplified successive-cancellation list technique to polar codes equivalent to the Golay code. The simulations have achieved the performance of a maximum likelihood decoding, with the low decoding complexity of polar codes, compared to one of the universal decoders of linear codes most known in the literature.

The implementation of Shannon-limited polar codes-based information reconciliation for quantum key distribution

Quantum key distribution (QKD) gives a way to generate unconditionally secure keys for two remote users, Alice and Bob. Information reconciliation (IR), which can correct the errors caused by the imperfections of the QKD systems, is a critical component in QKD. Due to the high-security requirements and large volumes of data processing, robustness and efficiency are two main factors that must be considered for the implementation of IR. The polar codes-based IR has several potential advantages, such as capacity to reach Shannon-limit, high IR efficiency, and low computational complexity. Although CPU-based IR is always implemented in most of the previous works, it is not the optimal implementation in terms of performance and power dissipation. To the best of our knowledge, there is still no work to build a special-purpose hardware module for polar codes-based IR. In this paper, a dedicated design of hardware accelerator is first proposed for polar codes-based IR, in which the block-checked successive cancellation list (SCL) algorithm is used to verify the consistency of the sifted keys, and the overall failure probability of IR is significantly reduced. The proposed design is constructed into a partially-unrolled parallel architecture to accelerate the core decoder as well as balance the resource utilization. Furthermore, the hardware implementation is completed based on Xilinx Zynq UltraScale+ XCZU5EV MPSoC platform and achieves an IR throughput of 15 Mbps with a block length of 212, while less than of the amount of on-chip resources are used in other previous designs of SCL decoder. The proposed design can provide a real-time, low-cost solution for IR in QKD systems, and enhance the performance of QKD.

A Tree Pruning Technique for Decoding Complexity Reduction of Polar Codes and PAC Codes

Sorting operation is one of the main bottlenecks for the successive-cancellation list (SCL) decoding. This paper introduces an improvement to the SCL decoding for polar and pre-transformed polar codes that reduces the number of sorting operations without visible degradation in the code’s error-correction performance. In an SCL decoding with an optimum metric function we show that, on average, the correct branch’s bit-metric value must be equal to the bit-channel capacity, and on the other hand, the average bit-metric value of a wrong branch can be at most zero. This implies that a wrong path’s partial path metric value deviates from the bit-channel capacity’s partial summation. For relatively reliable bit-channels, the bit metric for a wrong branch becomes very large negative number, which enables us to detect and prune such paths. We prove that, for a threshold lower than the bit-channel cutoff rate, the probability of pruning the correct path decreases exponentially by the given threshold. Based on these findings, we presented a pruning technique, and the experimental results demonstrate a substantial decrease in the amount of sorting procedures required for SCL decoding. In the stack algorithm, a similar technique is used to significantly reduce the average number of paths in the stack.

On the improvements of successive cancellation Creeper decoding for polar codes

In this paper, an improvement for successive cancellation (SC) decoding is presented for polar codes. This improvement is based on applying Creeper approach that was used to decode convolutional codes. The proposed decoder combines a stack and a Fano approaches, allowing to significantly decrease complexity of Successive Cancellation Fano decoder at the cost of a slight increase in space complexity. We also show how to combine the SC-Creeper decoding with a bit-flipping approach to further improve the performance of SC-Creeper due to introducing additional decoding attempts.Simulation results show that the proposed SC-Creeper and SC-Creeper Flip decoders with carefully selected parameters have the same performance as both CRC-aided Successive Cancellation List decoder with list size 8 and Fano decoder, while having much smaller complexity.

Application research of polar coded OFDM underwater acoustic communications

To further accelerate the practical process of polar codes in underwater acoustic communication (UWC) and improve the reliability and efficiency of underwater data transmission, we first propose a polar code construction method suitable for the underwater acoustic channel, which drastically reduces the complexity and meets the need for practical UWC. Then, we establish a practical polar coded UWC scheme by devising a two-step procedure based on the Orthogonal Frequency Division Multiplexing technique. Moreover, through simulation, the scheme's performances with the unimproved and the proposed polar code construction method are analyzed. Moreover, its performances with four different polar decoders are also given. The performance comparison with the LDPC coded UWC system is studied as well. Furthermore, lake-trial results under two different channel conditions demonstrate that the proposed construction method and the scheme effectively guarantee the reliability of data transmission, achieving error-free transmission at a transmission distance of 1718 m with the signal-to-noise-ratio (SNR) of 21 dB, and a transmission distance of 749 m with the SNR of 16.5 dB, better than the LDPC coded system with same conditions. The semi-experimental results show that the proposed polar coded system under the Cyclic Redundancy Check-Aided Successive Cancellation List decoder outperforms the LDPC coded system by approximately 2.1–3.7 dB.

Wireless Covert Communication with Polarization Dirty Constellation

Wireless covert communication is an emerging communication technique that prevents eavesdroppers. This paper presents a novel approach to wireless covert communication based on polar codes with dirty constellation polarization. The feasibility of dirty constellation polarization is analyzed, and the impact of covert transmission power on undetectability is investigated. We polarize the covert channel and decode the covert information using a successive-cancellation decoder. Simulation results demonstrate that polar codes can significantly improve the undetectability and reliability of covert communication when compared to BCH codes. Additionally, we find that polarized covert channels achieve better undetectability and reliability when using a successive-cancellation list decoder. The proposed algorithm shows significant improvement in the undetectability and reliability of wireless covert communication with dirty constellations. This research provides a promising direction for future development in the field of covert communication, with potential applications in secure communication systems.

List-serial pipelined hardware architecture for SCL decoding of polar codes

For polar codes, the performance of successive cancellation list (SCL) decoding is capable of approaching that of maximum likelihood decoding. However, the existing hardware architectures for the SCL decoding suffer from high hardware complexity due to calculating L decoding paths simultaneously, which are unfriendly to the devices with limited logical resources, such as field programmable gate arrays (FPGAs). In this paper, we propose a list-serial pipelined hardware architecture with low complexity for the SCL decoding, where the serial calculation and the pipelined operation are elegantly combined to strike a balance between the complexity and the latency. Moreover, we employ only one successive cancellation (SC) decoder core without L×L crossbars, and reduce the number of inputs of the metric sorter from 2L to L + 2. Finally, the FPGA implementations show that the hardware resource consumption is significantly reduced with negligible decoding performance loss.

Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding

A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction. Following this observation, successive cancellation decoding of such codes is introduced. In particular, the error probability of single parity-check product codes over binary memoryless symmetric channels under successive cancellation decoding is characterized. A bridge with the analysis of product codes introduced by Elias is also established for the binary erasure channel. Successive cancellation list decoding of single parity-check product codes is then described. For the provided example, simulations over the binary input additive white Gaussian channel show that successive cancellation list decoding outperforms belief propagation decoding applied to the code graph. Finally, the performance of the concatenation of a product code with a high-rate outer code is investigated via distance spectrum analysis. Examples of concatenations performing within 0.7 dB from the random coding union bound are provided.

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.