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

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.

Download Full-text

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.462-463.193 ◽

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.

Download Full-text

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.

Download Full-text

Bidirectional stack decoding of polar codes

Vojnotehnicki glasnik ◽

10.5937/vojtehg69-29858 ◽

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.

Download Full-text

Hamming Product Code Based Multiple Bit Error Correction Coding Scheme Using Keyboard Scan Based Decoding for on Chip Interconnects Links

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.241-244.2457 ◽

2012 ◽

Vol 241-244 ◽

pp. 2457-2461 ◽

Cited By ~ 2

Author(s):

Murali Maheswari ◽

Gopalakrishnan Seetharaman

Keyword(s):

Error Correction ◽

Error Rate ◽

Iterative Decoding ◽

Error Control ◽

Low Complexity ◽

Hardware Complexity ◽

Error Correction Coding ◽

Product Code ◽

Coding Scheme ◽

On Chip

In this paper, we present multiple bit error correction coding scheme using extended Hamming product code combined with type II HARQ and keyboard scan based error flipping to correct multiple bit errors for on chip interconnect. The keyboard scan based error flipping reduces the hardware complexity of the decoder compared to the existing three stages iterative decoding method for on chip interconnects. The proposed method of decoding achieves 86% of reduction in area and 23% of reduction in decoder delay with only small increase in residual flit error rate compared to the existing three stage iterative decoding scheme for multiple bit error correction. The proposed code also achieves excellent improvement in residual flit error rate and up to 66% of links power consumption compared to the other error control schemes. The low complexity and excellent residual flit error rate make the proposed code suitable for on chip interconnection links.

Download Full-text

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

Electronics ◽

10.3390/electronics11010093 ◽

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.

Download Full-text

Minimum Distance Optimization with Chord Edge Growth for High Girth Non-Binary LDPC Codes

Electronics ◽

10.3390/electronics9122161 ◽

2020 ◽

Vol 9 (12) ◽

pp. 2161

Author(s):

Changcai Han ◽

Hui Li ◽

Weigang Chen

Keyword(s):

Minimum Distance ◽

Signal To Noise Ratio ◽

High Reliability ◽

Ldpc Codes ◽

Full Rank ◽

Ldpc Code ◽

Low Complexity ◽

High Signal ◽

Rank Condition ◽

Potential Applications

Short or moderate-length non-binary low-density parity-check (NB-LDPC) codes have the potential applications in future low latency and high-reliability communication thanks to the strong error correction capability and parallel decoding. Because of the existence of the error floor, the NB-LDPC codes usually cannot satisfy very low bit error rate (BER) requirements. In this paper, a low-complexity method is proposed for optimizing the minimum distance of the NB-LDPC code in a progressive chord edge growth manner. Specifically, each chord edge connecting two non-adjacent vertices is added to the Hamiltonian cycle one-by-one. For each newly added chord edge, the configuration of non-zero entries corresponding to the chord edge is determined according to the so-called full rank condition (FRC) of all cycles that are related to the chord edge in the obtained subgraph. With minor modifications to the designed method, it can be used to construct the NB-LDPC codes with an efficient encoding structure. The analysis results show that the method for designing NB-LDPC codes while using progressive chord edge growth has lower complexity than traditional methods. The simulation results show that the proposed method can effectively improve the performance of the NB-LDPC code in the high signal-to-noise ratio (SNR) region. While using the proposed scheme, an NB-LDPC code with a quite low BER can be constructed with extremely low complexity.

Download Full-text

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

10.21203/rs.3.rs-203428/v1 ◽

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.

Download Full-text

Tailored Algorithms for the Detection of the Atmospheric Boundary Layer Height from Common Automatic Lidars and Ceilometers (ALC)

Remote Sensing ◽

10.3390/rs12193259 ◽

2020 ◽

Vol 12 (19) ◽

pp. 3259

Author(s):

Simone Kotthaus ◽

Martial Haeffelin ◽

Marc-Antoine Drouin ◽

Jean-Charles Dupont ◽

Sue Grimmond ◽

...

Keyword(s):

Boundary Layer ◽

Atmospheric Boundary Layer ◽

Signal To Noise Ratio ◽

Deep Convection ◽

High Signal ◽

Pollution Dispersion ◽

Low Snr ◽

Boundary Layer Height ◽

Cloud Dynamics ◽

New Generation

A detailed understanding of atmospheric boundary layer (ABL) processes is key to improve forecasting of pollution dispersion and cloud dynamics in the context of future climate scenarios. International networks of automatic lidars and ceilometers (ALC) are gathering valuable data that allow for the height of the ABL and its sublayers to be derived in near real time. A new generation of advanced methods to automatically detect the ABL heights now exist. However, diversity in ALC models means these algorithms need to be tailored to instrument-specific capabilities. Here, the advanced algorithm STRATfinder is presented for application to high signal-to-noise ratio (SNR) ALC observations, and results are compared to an automatic algorithm designed for low-SNR measurements (CABAM). The two algorithms are evaluated for application in an operational network setting. Results indicate that the ABL heights derived from low-SNR ALC have increased uncertainty during daytime deep convection, while high-SNR observations can have slightly reduced capabilities in detecting shallow nocturnal layers. Agreement between the ALC-based methods is similar when either is compared to the ABL heights derived from temperature profile data. The two independent methods describe very similar average diurnal and seasonal variations. Hence, high-quality products of ABL heights may soon become possible at national and continental scales.

Download Full-text

Crop yield prediction using data mining: an efficient data modeling approach

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i2.27.13157 ◽

2018 ◽

Vol 7 (2.27) ◽

pp. 128

Author(s):

Geetika . ◽

Rohit Bajaj

Keyword(s):

Data Mining ◽

Error Rate ◽

Signal To Noise Ratio ◽

Wheat Crop ◽

High Signal ◽

Agricultural Field ◽

Signal To Noise ◽

Linear Discriminant ◽

Noise Ratio ◽

Using Data

Motivation for this research comes from the agricultural point of view that there is a lot of work for the farmers to be done manually. So this research deals with the automatic classification approach which provides help to the farmers and decrease their efforts. With the change of climate in the world, the mainstreams of the crops in the agricultural field are severely affected in performance in previous decades. The crop prediction yielding should be healthy to help the farmers for taking suitable procedures for selling and loading/storage. Such estimations on the yielding of the crops will also assist the industries based on the farming and production of the crops for development of the logistics of their commercials. Numerous approaches of estimating and crop yielding have been established in the previous times with variable success rates. This paper deals with the prediction of the wheat crop yielding using data mining approaches. The paper deals with the clustering approach using k-means clustering and feature extraction using independent component analysis and the classification is done using linear discriminant analysis and the simulation is done using MATLAB environment. From the result and discussions it can be noticed that our proposed approach is able to achieve less error rate probabilities and high signal to noise ratio. The proposed approach is able to achieve mean square error rate of 0.5 and peak signal to noise ratio of 33.18 db.

Download Full-text

Improvement of Fast Simplified Successive-Cancellation Decoder for Polar Codes

Information ◽

10.3390/info9100254 ◽

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.

Download Full-text