scholarly journals A Novel Flip-List-Enabled Belief Propagation Decoder for Polar Codes

Electronics ◽  
2021 ◽  
Vol 10 (18) ◽  
pp. 2302
Author(s):  
Qasim Jan ◽  
Shahid Hussain ◽  
Muhammad Furqan ◽  
Zhiwen Pan ◽  
Nan Liu ◽  
...  
Keyword(s):  
Computational Complexity ◽  
Error Correction ◽  
Design Principle ◽  
Belief Propagation ◽  
State Of The Art ◽  
Signal To Noise Ratio ◽  
High Signal ◽  
Polar Codes ◽  
Successive Cancellation ◽  
Bit Flip

Due to the design principle of parallel processing, belief propagation (BP) decoding is attractive, and it provides good error-correction performance compared with successive cancellation (SC) decoding. However, its error-correction performance is still inferior to that of successive cancellation list (SCL) decoding. Consequently, this paper proposes a novel flip-list- (FL)-enabled belief propagation (BP) method to improve the error-correction performance of BP decoding for polar codes with low computational complexity. The proposed technique identifies the vulnerable channel log-likelihood ratio (LLR) that deteriorates the BP decoding result. The FL is utilized to efficiently identify the erroneous channel LLRs and correct them for the next BP decoding attempt. The preprocessed channel LLR through FL improves the error-correction performance with minimal flipping attempts and reduces the computational complexity. The proposed technique was compared with the state-of-the-art BP, i.e., BP bit-flip (BP-BF), generalized BP-flip (GBPF), cyclic redundancy check (CRC)-aided (CA-SCL) decoding, and ordered statistic decoding (OSD), algorithms. Simulation results showed that the FL-BP had an excellent block error rate (BLER) performance gain up to 0.7dB compared with BP, BP-BF, and GBPF decoder. Besides, the computational complexity was reduced considerably in the high signal-to-noise ratio (SNR) regime compared with the BP-BF and GBPF decoding methods.

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.

scholarly journals Improving Image Transmission by Using Polar Codes and Successive Cancellation List Decoding

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Álvaro Garcia ◽  
Maria De Lourdes Melo Guedes Alcoforado ◽  
Francisco Madeiro ◽  
Valdemar Cardoso Da Rocha Jr.
Keyword(s):  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Structural Similarity ◽  
Image Transmission ◽  
Polar Codes ◽  
Code Construction ◽  
Successive Cancellation ◽  
Natural Choice ◽  
Shift Keying

This paper investigates the transmission of grey scale images encoded with polar codes and de-coded with successive cancellation list (SCL) decoders in the presence of additive white Gaussian noise. Po-lar codes seem a natural choice for this application be-cause of their error-correction efficiency combined with fast decoding. Computer simulations are carried out for evaluating the influence of different code block lengths in the quality of the decoded images. At the encoder a default polar code construction is used in combination with binary phase shift keying modulation. The results are compared with those obtained by using the clas-sic successive cancellation (SC) decoding introduced by Arikan. The quality of the reconstructed images is assessed by using peak signal to noise ratio (PSNR) and the structural similarity (SSIM) index. Curves of PSNR and SSIM versus code block length are presented il-lustrating the improvement in performance of SCL in comparison with SC.

scholarly journals Improved Adaptive Successive Cancellation List Decoding of Polar Codes

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 899
Author(s):  
Xiumin Wang ◽  
Jinlong He ◽  
Jun Li ◽  
Zhuoting Wu ◽  
Liang Shan ◽  
...  
Keyword(s):  
Computational Complexity ◽  
Likelihood Ratio ◽  
Polar Codes ◽  
Correct Result ◽  
List Decoding ◽  
Successive Cancellation ◽  
Burst Error ◽  
Log Likelihood ◽  
Information Sequence ◽  
Simulation Results

Although the adaptive successive cancellation list (AD-SCL) algorithm and the segmented-CRC adaptive successive cancellation list (SCAD-SCL) algorithm based on the cyclic redundancy check (CRC) can greatly reduce the computational complexity of the successive cancellation list (SCL) algorithm, these two algorithms discard the previous decoding result and re-decode by increasing L, where L is the size of list. When CRC fails, these two algorithms waste useful information from the previous decoding. In this paper, a simplified adaptive successive cancellation list (SAD-SCL) is proposed. Before the re-decoding of updating value L each time, SAD-SCL uses the existing log likelihood ratio (LLR) information to locate the range of burst error bits, and then re-decoding starts at the incorrect bit with the smallest index in this range. Moreover, when the segmented information sequence cannot get the correct result of decoding, the SAD-SCL algorithm uses SC decoding to complete the decoding of the subsequent segmentation information sequence. Furthermore, its decoding performance is almost the same as that of the subsequent segmentation information sequence using the AD-SCL algorithm. The simulation results show that the SAD-SCL algorithm has lower computational complexity than AD-SCL and SCAD-SCL with negligible loss of performance.

scholarly journals Bit-Flip Algorithm for Successive Cancellation List Decoder of Polar Codes

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 58346-58352 ◽  
Author(s):  
Fengyi Cheng ◽  
Aijun Liu ◽  
Yingxian Zhang ◽  
Jing Ren
Keyword(s):  
Polar Codes ◽  
Successive Cancellation ◽  
Bit Flip ◽  
List Decoder

A Fast Adaptive Beamforming Algorithm Based on Gram-Schmidt Orthogonalization

2021 ◽  
Vol 16 (4) ◽  
pp. 642-650
Author(s):  
Bing-Feng Qian ◽  
Shi-Jie Gao ◽  
Quan-Feng Li ◽  
Qian Zhang ◽  
Ye Wang
Keyword(s):  
Computational Complexity ◽  
Covariance Matrix ◽  
Signal To Noise Ratio ◽  
Data Preprocessing ◽  
Adaptive Threshold ◽  
Adaptive Beamforming ◽  
High Signal ◽  
Signal To Noise ◽  
Schmidt Orthogonalization ◽  
Beamforming Algorithm

Fast implementation is one of the important indexes of the ADBF algorithm. The advantages of the Gram-Schmidt (GS) orthogonalization algorithm are that it can reconstruct the interference subspace well under the high signal-to-noise ratio and has fast convergence speed and low computational complexity. This paper studies the RGS algorithm for GS orthogonalization of sampling covariance matrix. To estimate the interference subspace more accurately, this paper modifies the orthogonal adaptive threshold of covariance matrix, and extends the proposed GS orthogonal algorithm of covariance matrix based on data preprocessing to the adaptive beamforming processing at subarray level.

Performance analysis of NR Polar Codes at short information blocks for control channels

2021 ◽  
Author(s):  
Tirthadip Sinha ◽  
Jaydeb Bhaumik
Keyword(s):  
Performance Analysis ◽  
Error Correction ◽  
Channel Coding ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Early Termination ◽  
Polar Codes ◽  
Cyclic Redundancy Check ◽  
Polar Code ◽  
Trade Offs

Abstract One important innovation in information and coding theory is polar code, which delivers capacity attaining error correction performance varying code rates and block lengths. In recent times, polar codes are preferred to offer channel coding in the physical control channels of the 5G (5 th Generation) wireless standard by 3GPP (Third Generation Partnership Project) New Radio (NR) group. Being a part of the physical layer, Channel coding plays key role in deciding latency and reliability of a communication system. However, the error correction performance degrades with decreased message lengths. 5G NR requires channel codes with low rates, very low error floors with short message lengths and low latency in coding process. In this work, Distributed Cyclic Redundancy Check Aided polar (DCA-polar) code along with Cyclic Redundancy Check Aided polar (CA-polar) code, the two variant of polar codes have been proposed which provide significant error-correction performance in the regime of short block lengths and enable early termination of decoding processes. While CRC bits improve the performance of SCL (successive cancellation list) decoding by increasing distance properties, distributed CRC bits permit path trimming and early-termination of the decoding process. The design can reduce the decoding latency and energy consumption of hardware, which is crucial for mobile applications like 5G. The work also considers the performance analysis of NR polar codes over AWGN (Additive White Gaussian Noise) for short information block lengths at low code rates in the uplink and downlink control channels using SNR (Signal to Noise Ratio) and FAR (False Alarm Rate) as the performance measures. Simulation results illustrate different trade-offs between error-correction and detection performances comparing proposed NR polar coding schemes.

scholarly journals Improvement of Fast Simplified Successive-Cancellation Decoder for Polar Codes

Information ◽  
2018 ◽  
Vol 9 (10) ◽  
pp. 254
Author(s):  
Chao Xing ◽  
Zhiliang Huang ◽  
Shengmei Zhao
Keyword(s):  
Reduction Method ◽  
Signal To Noise Ratio ◽  
Code Rate ◽  
Polar Codes ◽  
Latency Reduction ◽  
Low Snr ◽  
Successive Cancellation ◽  
Current Node ◽  
Reduction Methods ◽  
Check Condition

This paper presents a new latency reduction method for successive-cancellation (SC) decoding of polar codes that performs a frozen-bit checking on the rate-other (R-other) nodes of the Fast Simplified SC (Fast-SSC) pruning tree. The proposed method integrates the Fast-SSC algorithm and the Improved SSC method (frozen-bit checking of the R-other nodes). We apply a recognition-based method to search for as many constituent codes as possible in the decoding tree offline. During decoding, the current node can be decoded directly, if it is a special constituent code; otherwise, the frozen-bit check is executed. If the frozen-bit check condition is satisfied, the operation of the R-other node is the same as that of the rate-one node. In this paper, we prove that the frame error rate (FER) performance of the proposed algorithm is consistent with that of the original SC algorithm. Simulation results show that the proportion of R-other nodes that satisfy the frozen-bit check condition increases with the signal-to-noise-ratio (SNR). Importantly, our proposed method yields a significant reduction in latency compared to those given by existing latency reduction methods. The proposed method solves the problem of high latency for the Improved-SSC method at a high code rate and low SNR, simultaneously.

scholarly journals Area-Efficient Early-Termination Technique for Belief-Propagation Polar Decoders

Electronics ◽  
2019 ◽  
Vol 8 (9) ◽  
pp. 1001
Author(s):  
Choi ◽  
Yoo
Keyword(s):  
Error Correction ◽  
Bit Error Rate ◽  
Error Rate ◽  
Belief Propagation ◽  
Early Termination ◽  
Experimental Results ◽  
Polar Codes ◽  
Termination Criterion ◽  
Area Efficient

Early-termination techniques for a belief-propagation (BP) decoder of polar codes can improve the decoding throughput by finishing a decoding iteration when an early-termination condition is satisfied. In the BP decoders, the early-termination condition plays an important role, as it affects decoding iteration savings. In this letter, an area-efficient early-termination criterion is proposed, which simplifies the previous threshold-based termination condition by completely eliminating redundant computations. According to the experimental results, the proposed structure for (1024, 512) polar codes can reduce 72.7%, 66.5%, and 59.7% of hardware resources without any degradation in the error-correction performance and decoding throughput compared to the previous threshold-based, information-BER (bit error rate)-based, and frozen-BER-based early-termination techniques, respectively.

scholarly journals Combining belief propagation and successive cancellation list decoding of polar codes on a GPU platform

2017 ◽  
Author(s):  
Sebastian Cammerer ◽  
Benedikt Leible ◽  
Matthias Stahl ◽  
Jakob Hoydis ◽  
Stephan ten Brink
Keyword(s):  
Belief Propagation ◽  
Polar Codes ◽  
List Decoding ◽  
Successive Cancellation
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