Polar Decoder Research Articles

Hard-Decision SCL Polar Decoder With Weighted Pruning Operation for Storage Applications

Hard-Decision SCL Polar Decoder With Weighted Pruning Operation for Storage Applications

Highly reliable DHR-based polar compilation code communication method

The advent of fifth-generation mobile communication technology, 5G, has raised the bar for data transmission rates, information security, and reliability. Polar codes, the channel coding scheme in the 5G communication standard, encounter issues of singularity, limitations, and passivity in the face of unknown attacks. Therefore, this study introduces a highly reliable DHR-based polar coding communication approach. Drawing parallels between cyber attacks and channel noise, the method incorporates reconfigurable executors, decoding decisions, strategy scheduling, and other mechanisms to enable active defense. The True Relatively Axiom (TRA) is employed to theoretically validate the method’s heterogeneity, redundancy, and dynamics. Comparative simulation experiments with traditional polar decoding algorithms, such as SCL, SC, BP, SCAN, and SSC decoding algorithms, demonstrate that the proposed method not only improves secure transmission efficiency but also guarantees secure and reliable transmission across various attack scenarios. Our code is available at https://github.com/yuluzi/my-code.git.

Algorithmization and Hardware Implementation of Polar Coding for 5G Telecommunications

Abstract The article explores a recursive algorithm for determining Bhattacharyya parameters, which is a measure of the degree of channel polarization for telecommunications with polar coding. A method is given for determining the positions of information and fixed bits in a polar code. The principles of constructing a polar encoder and a polar decoder successive cancellation are considered. The Field-Programmable Gate Array implementation of the successive cancellation list decoder is considered. Experimental studies of the construction of a polar code using Gaussian approximation have been carried out. The influence of the design signal-to-noise ratio on the bit error rate of telecommunications with polar codes has been studied. The use of multi-position modulation in telecommunications with polar codes has been studied. It is expected that the results obtained will be useful in hardware and software implementation of 5G telecommunications with polar coding.

Chaotic Phase Modulation Direct-Sequence Spread Spectrum-Assisted Adaptive Serial Cancellation List Decoding Method for Underwater Acoustic Communication

Addressing the challenges of high decoding latency, reduced spectral efficiency, and substantial storage requirements in a Cyclic Redundancy Check (CRC)Aided Successive Cancellation List (CA-SCL) polar decoder, this paper proposes a chaotic phase modulation direct-sequence spread spectrum (CPMDSSS)-assisted adaptive serial cancellation list decoding method for underwater acoustic communication. The method involves segmenting the information bits to be transmitted, computing CRC for each segment, and mapping all CRCs to a CPMDSSS, which is then modulated onto the pilot subcarriers of underwater acoustic orthogonal frequency-division multiplexing (OFDM) to increase spectral efficiency. At the receiving end, CRCs are obtained by demodulating the CPMDSSS to verify the segmented information and adaptively select the number of decoding paths. The theoretical analysis and simulation results demonstrate that compared to CA-SCL, the proposed method effectively reduces the required storage units and improves spectral efficiency, with an average reduction of approximately 80% in the decoding paths. Sea trials further indicate that the proposed method reduces the average decoding paths by approximately 71% and decreases the average decoding delay by approximately 64% compared to CA-SCL.

Sequential Polar Decoding with Cost Metric Threshold

Polar codes have established themselves as a cornerstone in modern error correction coding due to their capacity-achieving properties and practical implementation advantages. However, decoding polar codes remains a computationally intensive task. In this paper, we introduce a novel approach to improve the decoding efficiency of polar codes by integrating the threshold-based SC-Creeper decoding algorithm, originally designed for convolutional codes. Our proposed decoder with an additional cost function seamlessly merges two established decoding paradigms, namely the stack and Fano approaches. The core idea is to leverage the strengths of both decoding techniques to strike a balance between computational efficiency and performance, with an additional method of controlling movement along a code tree. Simulations demonstrate the superiority of the proposed improved SC-Creeper decoder with tuned parameters. The improved SC-Creeper decoder achieves the performance of the CA-SCL-8 decoder in terms of high code rates and overcomes it in terms of the N=1024 code length, while simultaneously surpassing the efficiency of the traditional Fano decoding algorithm.

Fast Polar Decoding With Successive Cancellation List Creeper Algorithm

Fast Polar Decoding With Successive Cancellation List Creeper Algorithm

Efficient Hardware Realization of SC Polar Decoders Using Compound Pipelined Processing Units and Auxiliary Registers

Efficient Hardware Realization of SC Polar Decoders Using Compound Pipelined Processing Units and Auxiliary Registers

Data-driven Neural Polar Decoders for Unknown Channels with and without Memory

Data-driven Neural Polar Decoders for Unknown Channels with and without Memory

Polar-Coded Cooperation With Optimized Relay Selection in Multi-Satellite and Wireless Integrated Systems

Optimized polar-coded cooperation with an approximate prior probability-based threshold decision is proposed to improve the reliability and complexity in selective decode-and-forward (SDF) cooperation of multiple satellite constellation systems. First, an SDF scheme with polar coding is adopted in cooperative communications for efficient code construction and relay forwarding. Second, in the logarithmic belief propagation (BP) polar decoding, the variable iterative threshold is derived with independent and variable signal-to-noise ratio (SNR)-based approximate prior probability. This threshold reduces complexity by eliminating active nodes with high reliability in each decoding iteration. Third, the information detection factor is introduced to evaluate the accuracy of decoded bits, thereby limiting the average decoding iterations to improve decoding efficiency. Simulation results show that the proposed polar-coded SDF cooperation obtains 1.5 dB performance gain at a bit error rate (BER) of 10-3 compared with that of existing LDPC-related schemes. The complexity of the optimized logarithmic BP decoding is reduced by 25%–50% compared with that of the traditional BP decoding. Therefore, the proposed scheme has good BER performance and low complexity in cooperative communications of multi-satellite and wireless integrated systems.

Sparse graph neural network aided efficient decoder for polar codes under bursty interference

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 are shown that the proposed decoder is more robust than the existing ones in the presence of bursty interference and exhibits high universality.

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>

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.

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.

Error‐rate analysis of polar code designs using genetic algorithm for additive white Gaussian noise channel

SummaryA novel scheme for designing polar codes with specific decoding schemes in the additive white Gaussian noise channel is presented in this paper. The code construction strategy is built on the genetic algorithm (GA) where successive evolution of populations (or group of information sets) leads toward fittest candidate to attain finest error‐rates. In this work, it is shown that better error‐rates can be attained by both successive cancelation list decoding using GA with no cyclic redundancy check (CRC) and belief propagation decoding using GA with no CRC and no list, compared to existing polar decoding schemes. Our proposed polar code design scheme using GA has the ability to attain a target block error rates with the least possible SNR and using no additional CRC by exploiting least belief propagation iterations or lesser successive cancelation list list size with no self‐alterations in the decoding algorithm.

Performance Analysis of Successive Cancellation Decoder for Polar Codes with Two Stage Channel Estimator

Nowadays polar codes are becoming one of the most favorable capacity achieving Error Correction Codes (ECC) for their simple low encoding and decoding complexity, have received much attention in recent years; they probably achieve the theoretical capacity of discrete memoryless channels using the low complexity successive cancellation (SC) decoding algorithm. However, among the very few prior successive cancellation polar decoder designs, the required long code length makes the decoding latency high. As a new polar decoder, referred to as 2b-SC-Precomputation decoder, reduce the latency from (2n-1) to ((3n/4)-1) without performance loss, which can reduce the hardware complexity by two stage channel estimators. Furthermore, in our method, the decoding latency decreases rapidly with increasing throughput. Significant latency and throughput reductions are shown by simulation results and report synthesis results for ASIC.

Reliability-Design of Ordered Tree-Based Single-Parity-Check Decoder for Polar Codes Fast List Decoding

Reliability-Design of Ordered Tree-Based Single-Parity-Check Decoder for Polar Codes Fast List Decoding

FPGA Implementation of Flexible Successive-Cancellation Polar Decoder

Kanal kapasitesi, bir kanalın iletilebileceği maksimum bit hızını ifade eder. Kutupsal kodlar, simetrik ikili girişli, hafızasız kanallar için sonsuz blok uzunluğunda kanal kapasitesine erişebilen ilk hata düzeltme kodlarıdır. Kutupsal kodların bu başarımı ile 5. Nesil Yeni Radyo Haberleşme standardında kullanımına karar verilmiştir. Bu çalışmada, farklı blok uzunluklarında ve farklı kod oranlarında kutupsal kodların, ardışık-çıkarım (successive-cancellation) kod çözücü algoritması alanında programlanabilir kapı dizileri (Field-programmable gate array, FPGA) ile gerçeklemesi anlatılmıştır.

BP-Based Sparse Graph List Decoding of Polar Codes

How to construct an effective polar decoding scheme has attracted researchers in the field of communication. The belief propagation list (BPL) decoder has performance improvement over the traditional BP decoder but comes with much higher complexity. To solve the issue of high complexity & latency, a low-density parity-check (LDPC) like BP decoder was proposed but it suffered from performance degradation over the original BP decoder. In this paper, a BP-based sparse graph list (BP-SGL) decoder is proposed by leveraging both list decoding scheme and LDPC-like BP decoding algorithm to achieve performance improvement while maintaining low complexity & latency. The key idea of the proposed list generation method is the similarity comparison of decoding graphs. Testing results verify that selecting graphs with large structural differences helps to construct a list with good overall performance. Simulation results show that the proposed scheme is superior to LDPC-like BP, and even outperforms the original BPL and some state-of-the-art (SOTA) BP-based decoding algorithms with significant reduction in complexity & latency.

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.

Low-Latency SCL Polar Decoder Architecture Using Overlapped Pruning Operations

Allowing the superior error-correction performance even for short-length codewords, the successive-cancellation list (SCL) decoding algorithm has allowed the polar code to be adopted in 5G New Radio standard for control channel. However, existing SCL polar decoders still suffer from long processing latency caused by a number of serialized internal operations. In this work, to solve the latency problem, we present several parallel computing solutions for the serialized operations, i.e., simplified data dependencies and two overlapped pruning operations. To realize the proposed parallel computing, we also introduce internal circuit blocks including dual read-port buffers, an on-the-fly parity checker, and overlapped processing units. The proposed SCL polar decoders are precisely designed with optimal design parameters by analyzing trade-offs between the latency reduction and area overheads. Implemented in a 65-nm CMOS technology, the proposed list-8 SCL polar decoder requires only 374 ns to handle a (1024, 512) 5G codeword, improving the decoding efficiency by 34.7% compared to the previous designs.