scholarly journals Novel Low Complexity BP Decoding Algorithms for Polar Codes: Simplifying on Non-Linear Operations

Electronics ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 93
Author(s):  
Yuhuan Wang ◽  
Jianguo Li ◽  
Neng Ye ◽  
Xiangyuan Bu
Keyword(s):  
Computational Complexity ◽  
Hardware Implementation ◽  
Low Complexity ◽  
Bp Algorithm ◽  
Polar Codes ◽  
Decoding Algorithm ◽  
Hyperbolic Tangent ◽  
Decoding Algorithms ◽  
Tangent Function ◽  
Non Linear

The parallel nature of the belief propagation (BP) decoding algorithm for polar codes opens up a real possibility of high throughput and low decoding latency during hardware implementation. To address the problem that the BP decoding algorithm introduces high-complexity non-linear operations in the iterative messages update process, this paper proposes to simplify these operations and develops two novel low complexity BP decoding algorithms, namely, exponential BP (Exp-BP) decoding algorithm and quantization function BP (QF-BP) decoding algorithm. The proposed algorithms simplify the compound hyperbolic tangent function by using probability distribution fitting techniques. Specifically, the Exp-BP algorithm simplifies two types of non-linear operations into single non-linear operation using the piece-wise exponential model function, which can approximate the hyperbolic tangent function in the updating formula. The QF-BP algorithm eliminates non-linear operations using the non-uniform quantization in the updating formula, which is effective in reducing computational complexity. According to the simulation results, the proposed algorithms can reduce the computational complexity up to 50% in each iteration with a loss of less than 0.1 dB compared with the BP decoding algorithm, which can facilitate the hardware implementation.

scholarly journals Bidirectional stack decoding of polar codes

2021 ◽  
Vol 69 (2) ◽  
pp. 405-415
Author(s):  
Aleksandar Minja ◽  
Dušan Dobromirov ◽  
Vojin Šenk
Keyword(s):  
Error Correction ◽  
High Speed ◽  
Parallel Implementation ◽  
Convolutional Codes ◽  
Low Complexity ◽  
Low Latency ◽  
Polar Codes ◽  
Decoding Algorithm ◽  
Decoding Algorithms ◽  
Successive Cancellation

Introduction/purpose: The paper introduces a reduced latency stack decoding algorithm of polar codes, inspired by the bidirectional stack decoding of convolutional codes and based on the folding technique. Methods: The stack decoding algorithm (also known as stack search) that is useful for decoding tree codes, the list decoding technique introduced by Peter Elias and the folding technique for polar codes which is used to reduce the latency of the decoding algorithm. The simulation was done using the Monte Carlo procedure. Results: A new polar code decoding algorithm, suitable for parallel implementation, is developed and the simulation results are presented. Conclusions: Polar codes are a class of capacity achieving codes that have been adopted as the main coding scheme for control channels in 5G New Radio. The main decoding algorithm for polar codes is the successive cancellation decoder. This algorithm performs well at large blocklengths with a low complexity, but has very low reliability at short and medium blocklengths. Several decoding algorithms have been proposed in order to improve the error correcting performance of polar codes. The successive cancellation list decoder, in conjunction with a cyclic redundancy check, provides very good error-correction performance, but at the cost of a high implementation complexity. The successive cancellation stack decoder provides similar error-correction performance at a lower complexity. Future machine-type and ultra reliable low latency communication applications require high-speed low latency decoding algorithms with good error correcting performance. In this paper, we propose a novel decoding algorithm, inspired by the bidirectional stack decoding of classical convolutional codes, with reduced latency that achieves similar performance as the classical successive cancellation list and successive cancellation stack decoding algorithms. The results are presented analytically and verified by simulation.

scholarly journals A Low-Complexity Ordered Statistics Decoding Algorithm for Short Polar Codes

2019 ◽  
Vol 9 (5) ◽  
pp. 831
Author(s):  
Yusheng Xing ◽  
Guofang Tu
Keyword(s):  
Error Correction ◽  
Error Rate ◽  
Complexity Analysis ◽  
Signal To Noise Ratio ◽  
Low Complexity ◽  
High Signal ◽  
Polar Codes ◽  
Decoding Algorithm ◽  
Low Snr ◽  
Ordered Statistics

In this paper, we propose a low-complexity ordered statistics decoding (OSD) algorithm called threshold-based OSD (TH-OSD) that uses a threshold on the discrepancy of the candidate codewords to speed up the decoding of short polar codes. To determine the threshold, we use the probability distribution of the discrepancy value of the maximal likelihood codeword with a predefined parameter controlling the trade-off between the error correction performance and the decoding complexity. We also derive an upper-bound of the word error rate (WER) for the proposed algorithm. The complexity analysis shows that our algorithm is faster than the conventional successive cancellation (SC) decoding algorithm in mid-to-high signal-to-noise ratio (SNR) situations and much faster than the SC list (SCL) decoding algorithm. Our addition of a list approach to our proposed algorithm further narrows the error correction performance gap between our TH-OSD and OSD. Our simulation results show that, with appropriate thresholds, our proposed algorithm achieves performance close to OSD’s while testing significantly fewer codewords than OSD, especially with low SNR values. Even a small list is sufficient for TH-OSD to match OSD’s error rate in short-code scenarios. The algorithm can be easily extended to longer code lengths.

A BP Decoding Algorithm Based on Nodes Residual for LDPC Codes and its Hardware Implementation

2011 ◽  
Vol 128-129 ◽  
pp. 7-10
Author(s):  
Zhong Xun Wang ◽  
Xing Cheng Wang ◽  
Fang Qiang Zhu
Keyword(s):  
Hardware Implementation ◽  
Belief Propagation ◽  
Dynamic Scheduling ◽  
Ldpc Codes ◽  
Ldpc Code ◽  
Low Complexity ◽  
Decoding Algorithm ◽  
Fast Decoding ◽  
Good For

We researched BP decoding algorithm based on variable-to-check information residual for LDPC code (VC-RBP) in this paper. It is a dynamic scheduling belief propagation using residuals, and has some advantages，such as fast decoding, good performance, and low complexity. It is similar to residual belief propagation (RBP),but has some difference in computing the residual message. This paper further optimized the new algorithm on DSP of TMS320dm6446, and it is good for hardware implementation.

A Min-Sum Algorithm Suitable for Hardware Implementation Based on LDPC Codes

2011 ◽  
Vol 271-273 ◽  
pp. 458-463
Author(s):  
Rui Ping Chen ◽  
Zhong Xun Wang ◽  
Xin Qiao Yu
Keyword(s):  
Hardware Implementation ◽  
Ldpc Codes ◽  
Low Complexity ◽  
Scaling Factor ◽  
Computation Complexity ◽  
Decoding Complexity ◽  
Decoding Algorithms ◽  
Hardware Resource ◽  
Simulation Results ◽  
Ber Performance

Decoding algorithms with strong practical value not only have good decoding performance, but also have the computation complexity as low as possible. For this purpose, the paper points out the modified min-sum decoding algorithm(M-MSA). On the condition of no increasing in the decoding complexity, it makes the error-correcting performance improved by adding the appropriate scaling factor based on the min-sum algorithm(MSA), and it is very suitable for hardware implementation. Simulation results show that this algorithm has good BER performance, low complexity and low hardware resource utilization, and it would be well applied in the future.

scholarly journals A Parallel Decoding Algorithm for Short Polar Codes Based on Error Checking and Correcting

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Yingxian Zhang ◽  
Xiaofei Pan ◽  
Kegang Pan ◽  
Zhan Ye ◽  
Chao Gong
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Polar Codes ◽  
Code Length ◽  
Decoding Algorithm ◽  
Parallel Method ◽  
Decoding Algorithms ◽  
Parallel Decoding ◽  
Error Checking ◽  
Maximization Principle

We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive theerror-checking equationsgenerated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of theerror-checking equations, we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length.

Study of FCLSD Algorithm Performance Based on LTE System

2012 ◽  
Vol 195-196 ◽  
pp. 96-103
Author(s):  
Ke Wen Liu ◽  
Quan Liu
Keyword(s):  
High Performance ◽  
Hardware Implementation ◽  
Low Complexity ◽  
Detection Algorithm ◽  
Sphere Decoding ◽  
Mimo Detection ◽  
Decoding Algorithm ◽  
Algorithm Performance ◽  
Simulation Results ◽  
Ber Performance

Soft-output complex list sphere decoding algorithm is a low-complexity MIMO detection algorithm and its BER performance approximates that of Maximum-Likelihood. However, it has a problem of not fixed complexity, and which make it very difficult to implement. To resolve this and try best to retain the advantages of the algorithm, a modified algorithmfixed complex list sphere decoding algorithm was proposed. Based on LTE TDD system, this paper studies the performance of the FCLSD algorithm. The simulation results show that: the BER performance of the FCLSD algorithm is close to that of the CLSD algorithm. However, when the number of antennas and modulation order increasing, the FCLSD algorithm is non-constrained of spherical radius and has fixed complexity. In addition, hardware implementation of the FCLSD algorithm could be carried out by parallel processing, thereby greatly reducing the algorithm complexity. So it is a high-performance algorithm of great potential.

scholarly journals Flexible soft-output decoding of polar codes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sunghoon Lee ◽  
Jooyoun Park ◽  
Il-Min Kim ◽  
Jun Heo
Keyword(s):  
Belief Propagation ◽  
Low Complexity ◽  
Low Latency ◽  
Polar Codes ◽  
High Complexity ◽  
Decoding Algorithms ◽  
Long Latency ◽  
System Requirement ◽  
System Requirements ◽  
High Computational Complexity

AbstractIn this research, we study soft-output decoding of polar codes. Two representative soft-output decoding algorithms are belief propagation (BP) and soft cancellation (SCAN). The BP algorithm has low latency but suffers from high computational complexity. On the other hand, the SCAN algorithm, which is proposed for reduced complexity of soft-output decoding, achieves good decoding performance but suffers from long latency. These two algorithms are suitable only for two extreme cases that need very low latency (but with high complexity) or very low complexity (but with high latency). However, many practical systems may need to work for the moderate cases (i.e., not too high latency and not too high complexity) rather than two extremes. To adapt to the various needs of the systems, we propose a very flexible soft-output decoding framework of polar codes. Depending on which system requirement is most crucial, the proposed scheme can adapt to the systems by controlling the level of parallelism. Numerical results demonstrate that the proposed scheme can effectively adapt to various system requirements by changing the level of parallelism.

A Novel LLR-BP Algorithm for LDPC Codes Based on Taylor Series and Least Squares

2013 ◽  
Vol 462-463 ◽  
pp. 193-197
Author(s):  
Xing Ru Zhang ◽  
Jian Ping Li ◽  
Chao Shi Cai
Keyword(s):  
Least Squares ◽  
Taylor Series ◽  
Belief Propagation ◽  
Signal To Noise Ratio ◽  
Ldpc Codes ◽  
Low Complexity ◽  
Significant Loss ◽  
Bp Algorithm ◽  
High Signal ◽  
Decoding Algorithm

An effective log-likelihood-ratio-based belief propagation (LLR-BP) algorithm is proposed. It can reduce computational complexity of decoding algorithm for Low Density Parity Check (LDPC) codes. By using the Taylor series and least squares, high order multiplication based on the hyperbolic tangent (tanh) rule is converted to a first-order multiplication and addition after simplification. Moreover, all the logarithmic and exponential operations disappear without significant loss of the decoding performance. The simulation results show that the performance of the proposed scheme is similar to the general LLR-BP. In particular, we show that the modified algorithm with low complexity can achieve better BER than the other decoding algorithm in high signal-to-noise ratio region.

scholarly journals A Generalization Belief Propagation Decoding Algorithm for Polar Codes Based on Particle Swarm Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yingxian Zhang ◽  
Aijun Liu ◽  
Xiaofei Pan ◽  
Shi He ◽  
Chao Gong
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problem ◽  
Belief Propagation ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Polar Codes ◽  
Decoding Algorithm ◽  
Swarm Optimization ◽  
Decoding Algorithms ◽  
Modifying Factors

We propose a generalization belief propagation (BP) decoding algorithm based on particle swarm optimization (PSO) to improve the performance of the polar codes. Through the analysis of the existing BP decoding algorithm, we first introduce a probability modifying factor to each node of the BP decoder, so as to enhance the error correcting capacity of the decoding. Then, we generalize the BP decoding algorithm based on these modifying factors and drive the probability update equations for the proposed decoding. Based on the new probability update equations, we show the intrinsic relationship of the existing decoding algorithms. Finally, in order to achieve the best performance, we formulate an optimization problem to find the optimal probability modifying factors for the proposed decoding algorithm. Furthermore, a method based on the modified PSO algorithm is also introduced to solve that optimization problem. Numerical results show that the proposed generalization BP decoding algorithm achieves better performance than that of the existing BP decoding, which suggests the effectiveness of the proposed decoding algorithm.

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