Improvement of Fast Simplified Successive-Cancellation Decoder for Polar Codes

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.

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

Annals of Disaster Risk Sciences ◽

10.51381/adrs.v3i1.41 ◽

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.

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

Applied Sciences ◽

10.3390/app9050831 ◽

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.

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Channel Coding for Multi-Carrier Wireless Partial Duplex

Wireless Communications and Mobile Computing ◽

10.1155/2019/9891821 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13

Author(s):

Hamid R. Barzegar ◽

Luca Reggiani

Keyword(s):

Turbo Codes ◽

Channel Coding ◽

Orthogonal Frequency Division Multiplexing ◽

Signal To Noise Ratio ◽

A Priori ◽

Full Duplex ◽

Polar Codes ◽

Satisfactory Solution ◽

Low Snr ◽

Half Duplex

In order to leverage the spectrum resources, several forms of wireless duplex have been introduced and investigated in recent years. In Partial Duplex (PD) schemes, part of the band is transmitted in Full-Duplex (FD) and the rest in Half-Duplex (HD); therefore, some transmitted symbols will be characterized, at the receiver, by high SNR (Signal-to-Noise Ratio) and others by low SNR because of the residual self-interference (SI) in the FD part. Combining properly the patterns of these high and low SNR symbols affects the performance of the encoding schemes used in the system; in order to overcome this issue, different encoding and allocation schemes can be adopted for achieving a satisfactory solution. This paper investigates the performance of Low-Density Parity-Check (LDPC), turbo, polar codes for wireless PD. Orthogonal Frequency Division Multiplexing (OFDM) is an efficient multicarrier modulation technique, used in 4G and in the upcoming 5G, and it can be exploited for realizing a proper symbol allocation according to the SNR on each subcarrier. In this context, performance of LDPC, polar, and turbo codes derived from existing specifications has been studied when the system faces a mixture of high and low SNRs on the bits and hence on the symbols coming from the same codeword and this unbalanced SNR distribution is known a-priori at the transmitter, a condition associated with a scheme in which part of the symbols is subject to FD interference.

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Accuracy improvement of phase estimation in electron holography using noise reduction methods

Microscopy ◽

10.1093/jmicro/dfz115 ◽

2020 ◽

Vol 69 (2) ◽

pp. 123-131 ◽

Cited By ~ 1

Author(s):

Yoshihiro Midoh ◽

Koji Nakamae

Keyword(s):

Noise Reduction ◽

Reduction Method ◽

Signal To Noise Ratio ◽

Wiener Filter ◽

Phase Estimation ◽

Electron Holography ◽

Electron Dose ◽

Evaluation Indexes ◽

Reduction Methods ◽

Fourier Transform Phase

Abstract We try to improve the limit of the phase estimation of the interference fringe at low electron dose levels in electron holography by a noise reduction method. In this paper, we focus on unsupervised approaches to apply it to electron beam-sensitive and unknown samples and describe an overview of denoising methods used widely in image processing, such as wiener filter, total variation denoising, nonlocal mean filters and wavelet thresholding. We compare the wavelet hidden Markov model (WHMM) denoising that we have studied so far with the other conventional noise reduction methods. We evaluate the denoise performance of each method using the peak signal-to-noise ratio between noise-free and the target holograms (noisy or denoised holograms) and the root mean-square error (RMSE) between the true phase of the fringe and the measured phase by the discrete Fourier transform phase estimator. We show the denoised holograms for simulation and experimental data by using each noise reduction method and then discuss evaluation indexes obtained from these denoised holograms. From experimental results, it can be seen that the WHMM denoising can reduce the RMSE of fringe phase to about 1/4.5 for noisy simulation holograms and it has stable and good performance for noise reduction of observed holograms with various image qualities.

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List Decoding of Arıkan’s PAC Codes

Entropy ◽

10.3390/e23070841 ◽

2021 ◽

Vol 23 (7) ◽

pp. 841

Author(s):

Hanwen Yao ◽

Arman Fazeli ◽

Alexander Vardy

Keyword(s):

Superior Performance ◽

Polar Codes ◽

Dramatic Improvement ◽

List Decoding ◽

Sequential Decoding ◽

Worst Case ◽

Low Snr ◽

Successive Cancellation ◽

Polar Coding ◽

Wide Range

Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short blocklengths under standard successive cancellation decoding is far from optimal. A well-known way to improve the performance of polar codes at short blocklengths is CRC precoding followed by successive-cancellation list decoding. This approach, along with various refinements thereof, has largely remained the state of the art in polar coding since it was introduced in 2011. Recently, Arıkan presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. At short blocklengths, such codes offer a dramatic improvement in performance as compared to CRC-aided list decoding of conventional polar codes. PAC codes are based primarily upon the following main ideas: replacing CRC codes with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. One of our primary goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size L is moderately large (say, L⩾128). List decoding has distinct advantages over sequential decoding in certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, and use these estimates to approximate the union bound on their performance. These results indicate that PAC codes are superior to both polar codes and Reed–Muller codes. We also consider random time-varying convolutional precoding for PAC codes, and observe that this scheme achieves the same superior performance with constraint length as low as ν=2.

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Memory Requirement Reduction Method for Successive Cancellation Decoding of Polar Codes

Journal of Signal Processing Systems ◽

10.1007/s11265-016-1179-5 ◽

2016 ◽

Vol 88 (3) ◽

pp. 425-438

Author(s):

Guillaume Berhault ◽

Camille Leroux ◽

Christophe Jego ◽

Dominique Dallet

Keyword(s):

Reduction Method ◽

Polar Codes ◽

Memory Requirement ◽

Successive Cancellation ◽

Successive Cancellation Decoding

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

Electronics ◽

10.3390/electronics10182302 ◽

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.

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Performance Analysis of CRC Codes for Systematic and Nonsystematic Polar Codes with List Decoding

Wireless Communications and Mobile Computing ◽

10.1155/2018/7286909 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Takumi Murata ◽

Hideki Ochiai

Keyword(s):

Error Detection ◽

Signal To Noise Ratio ◽

Candidate Selection ◽

Polar Codes ◽

List Decoding ◽

Decoding Algorithms ◽

Outer Code ◽

Successive Cancellation ◽

Code Structure ◽

Proper Length

Successive cancellation list (SCL) decoding of polar codes is an effective approach that can significantly outperform the original successive cancellation (SC) decoding, provided that proper cyclic redundancy-check (CRC) codes are employed at the stage of candidate selection. Previous studies on CRC-assisted polar codes mostly focus on improvement of the decoding algorithms as well as their implementation, and little attention has been paid to the CRC code structure itself. For the CRC-concatenated polar codes with CRC code as their outer code, the use of longer CRC code leads to reduction of information rate, whereas the use of shorter CRC code may reduce the error detection probability, thus degrading the frame error rate (FER) performance. Therefore, CRC codes of proper length should be employed in order to optimize the FER performance for a given signal-to-noise ratio (SNR) per information bit. In this paper, we investigate the effect of CRC codes on the FER performance of polar codes with list decoding in terms of the CRC code length as well as its generator polynomials. Both the original nonsystematic and systematic polar codes are considered, and we also demonstrate that different behaviors of CRC codes should be observed depending on whether the inner polar code is systematic or not.

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Study of the operational SNR while constructing polar codes

International Journal of Electrical and Computer Engineering (IJECE) ◽

10.11591/ijece.v10i3.pp3200-3207 ◽

2020 ◽

Vol 10 (3) ◽

pp. 3200

Author(s):

Reda Benkhouya ◽

Idriss Chana ◽

Youssef Hadi

Keyword(s):

Channel Coding ◽

Communication Systems ◽

Error Control ◽

Signal To Noise Ratio ◽

Code Rate ◽

Polar Codes ◽

Error Control Coding ◽

Polar Coding ◽

Discrete Search ◽

Forward Error

Channel coding is commonly based on protecting information to be communicated across an unreliable medium, by adding patterns of redundancy into the transmission path. Also referred to as forward error control coding (FECC), the technique is widely used to enable correcting or at least detecting bit errors in digital communication systems. In this paper we study an original FECC known as polar coding which has proven to meet the typical use cases of the next generation mobile standard. This work is motivated by the suitability of polar codes for the new coming wireless era. Hence, we investigate the performance of polar codes in terms of bit error rate (BER) for several codeword lengths and code rates. We first perform a discrete search to find the best operating signal-to-noise ratio (SNR) at two different code rates, while varying the blocklength. We find in our extensive simulations that the BER becomes more sensitive to operating SNR (OSNR) as long as we increase the blocklength and code rate. Finally, we note that increasing blocklength achieves an SNR gain, while increasing code rate changes the OSNR domain. This trade-off sorted out must be taken into consideration while designing polar codes for high-throughput application.

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