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.

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 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 A Low-Complexity Belief Propagation Based Decoding Scheme for Polar Codes - Decodability Detection and Early Stopping Prediction

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 159808-159820 ◽  
Author(s):  
Yaohan Wang ◽  
Shunqing Zhang ◽  
Chuan Zhang ◽  
Xiaojing Chen ◽  
Shugong Xu
Keyword(s):  
Belief Propagation ◽  
Low Complexity ◽  
Polar Codes ◽  
Early Stopping

Relaxed Polar Codes under AWGN Channels with Low Complexity and Low Latency

2019 ◽  
Author(s):  
Xinyi Wang ◽  
Ce Sun ◽  
Jingxuan Huang ◽  
Dai Jia ◽  
Yifan Jiang ◽  
...  
Keyword(s):  
Low Complexity ◽  
Low Latency ◽  
Polar Codes

scholarly journals Priority Queue VLSI Architecture for Sequential Decoder of Polar Codes

2021 ◽  
Author(s):  
Andrey Rashich ◽  
Aleksei Krylov ◽  
Dmitrii Fadeev ◽  
Kirill Sinjutin
Keyword(s):  
Vlsi Architecture ◽  
Priority Queue ◽  
Low Complexity ◽  
Low Latency ◽  
Polar Codes ◽  
Sorting Networks ◽  
Vlsi Architectures ◽  
Simulation Results ◽  
Full Search ◽  
Ber Performance

<div>The VLSI architectures for stack or priority queue (PQ) are required in the implementation of stack or sequential decoders of polar codes. Such type of decoders provide good BER performance keeping complexity low. Extracting the best and the worst paths from PQ is the most complex operation in terms of both latency and complexity, because this operation requires full search along priority queue. In this work we propose a low latency and low complexity parallel hardware architecture for PQ, which is based on the systolic sorter and simplified sorting primitives. The simulation results show that just small BER degradation is introduced compared to ideal full sorting networks. Proposed PQ architecture is implemented in FPGA, the synthesis results are presented for all components of PQ.</div>

scholarly journals Weighted-Bit-Flipping-Based Sequential Scheduling Decoding Algorithms for LDPC Codes

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Qing Zhu ◽  
Le-nan Wu
Keyword(s):  
Belief Propagation ◽  
Scheduling Algorithm ◽  
Simple Algorithm ◽  
Ldpc Codes ◽  
Satellite Communications ◽  
Low Complexity ◽  
Computation Complexity ◽  
Tanner Graph ◽  
Decoding Algorithms ◽  
Video Broadcasting

Low-density parity-check (LDPC) codes can be applied in a lot of different scenarios such as video broadcasting and satellite communications. LDPC codes are commonly decoded by an iterative algorithm called belief propagation (BP) over the corresponding Tanner graph. The original BP updates all the variable-nodes simultaneously, followed by all the check-nodes simultaneously as well. We propose a sequential scheduling algorithm based on weighted bit-flipping (WBF) algorithm for the sake of improving the convergence speed. Notoriously, WBF is a low-complexity and simple algorithm. We combine it with BP to obtain advantages of these two algorithms. Flipping function used in WBF is borrowed to determine the priority of scheduling. Simulation results show that it can provide a good tradeoff between FER performance and computation complexity for short-length LDPC codes.

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.

scholarly journals Priority Queue VLSI Architecture for Sequential Decoder of Polar Codes

2021 ◽  
Author(s):  
Andrey Rashich ◽  
Aleksei Krylov ◽  
Dmitrii Fadeev ◽  
Kirill Sinjutin
Keyword(s):  
Vlsi Architecture ◽  
Priority Queue ◽  
Low Complexity ◽  
Low Latency ◽  
Polar Codes ◽  
Sorting Networks ◽  
Vlsi Architectures ◽  
Simulation Results ◽  
Full Search ◽  
Ber Performance

<div>The VLSI architectures for stack or priority queue (PQ) are required in the implementation of stack or sequential decoders of polar codes. Such type of decoders provide good BER performance keeping complexity low. Extracting the best and the worst paths from PQ is the most complex operation in terms of both latency and complexity, because this operation requires full search along priority queue. In this work we propose a low latency and low complexity parallel hardware architecture for PQ, which is based on the systolic sorter and simplified sorting primitives. The simulation results show that just small BER degradation is introduced compared to ideal full sorting networks. Proposed PQ architecture is implemented in FPGA, the synthesis results are presented for all components of PQ.</div>

Compact specification of polar codes

2019 ◽  
pp. 40-47
Author(s):  
R. A. Morozov ◽  
P. V. Trifonov
Keyword(s):  
Storage Capacity ◽  
Low Complexity ◽  
Practical Implementation ◽  
Polar Codes ◽  
Practical Relevance ◽  
Memory Consumption ◽  
Full Size ◽  
The Family ◽  
Erasure Probability ◽  
Binary Erasure Channel

Introduction:Practical implementation of a communication system which employs a family of polar codes requires either to store a number of large specifications or to construct the codes by request. The first approach assumes extensive memory consumption, which is inappropriate for many applications, such as those for mobile devices. The second approach can be numerically unstable and hard to implement in low-end hardware. One of the solutions is specifying a family of codes by a sequence of subchannels sorted by reliability. However, this solution makes it impossible to separately optimize each code from the family.Purpose:Developing a method for compact specifications of polar codes and subcodes.Results:A method is proposed for compact specification of polar codes. It can be considered a trade-off between real-time construction and storing full-size specifications in memory. We propose to store compact specifications of polar codes which contain frozen set differences between the original pre-optimized polar codes and the polar codes constructed for a binary erasure channel with some erasure probability. Full-size specification needed for decoding can be restored from a compact one by a low-complexity hardware-friendly procedure. The proposed method can work with either polar codes or polar subcodes, allowing you to reduce the memory consumption by 15–50 times.Practical relevance:The method allows you to use families of individually optimized polar codes in devices with limited storage capacity. 

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