LDPC Codes with the Layered LLR-BP Algorithm for 3GPP

2013 ◽  
Vol 462-463 ◽  
pp. 720-723
Author(s):  
Miao Miao Li ◽  
Jian Ping Li ◽  
Chao Shi Cai
Keyword(s):  
Belief Propagation ◽  
Ldpc Codes ◽  
Bp Algorithm ◽  
Parity Check ◽  
Computation Complexity ◽  
Decoding Algorithm ◽  
Absolute Value ◽  
Low Density Parity Check ◽  
Variable Node ◽  
Log Likelihood

We propose a layered log-likelihood-ratio-based belief propagation(LLR-BP)algorithm for Low Density Parity Check (LDPC)codes. In the conventional decoding algorithm, the process of decoding would be terminated when it reaches the maximum iterative number or the near-convergence is achieved. The proposed algorithm is based on the variable node information quantification and stop updating criterion thought. By dividing the absolute value of the variable node to different layers, a part of the check nodes stop the iteration before reaching the maximum iterative number to save iterative time. From the simulation results, we know that the improved decoding algorithm successively achieves lower computation complexity than the conventional one .And the layered LLR-BP algorithm is a better scheme for LDPC codes.

scholarly journals Design of Quasi-Cyclic Low Density Parity Check Decoder Using Optimized Min-Sum Algorithm

2018 ◽  
Vol 7 (03) ◽  
pp. 23781-23784
Author(s):  
Rajarshini Mishra
Keyword(s):  
Variance Estimation ◽  
Cyclic Codes ◽  
Ldpc Codes ◽  
Ldpc Code ◽  
Low Complexity ◽  
Low Density ◽  
Parity Check ◽  
Decoding Algorithm ◽  
Low Density Parity Check ◽  
Xilinx Fpga

Low-density parity-check (LDPC) have been shown to have good error correcting performance approaching Shannon’s limit. Good error correcting performance enables efficient and reliable communication. However, a LDPC code decoding algorithm needs to be executed efficiently to meet cost , time, power and bandwidth requirements of target applications. Quasi-cyclic low-density parity-check (QC-LDPC) codes are an important subclass of LDPC codes that are known as one of the most effective error controlling methods. Quasi cyclic codes are known to possess some degree of regularity. Many important communication standards such as DVB-S2 and 802.16e use these codes. The proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.Proposed decoder is well matched for VLSI implementation and will be implemented on Xilinx FPGA family

scholarly journals A Doping Bits Based BP Decoding for Rateless Distributed Source Coding Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
N. M. Masoodhu Banu ◽  
S. Sasikumar
Keyword(s):  
Belief Propagation ◽  
Source Coding ◽  
Ldpc Codes ◽  
Distributed Source Coding ◽  
Decoding Algorithm ◽  
Likelihood Ratios ◽  
Regular Source ◽  
Log Likelihood ◽  
Rate Adaptive ◽  
Decoder Complexity

A novel doping bits based belief propagation decoding algorithm, for rate-adaptive LDPC codes based on fixed bipartite graph code, is proposed. The proposed work modifies the decoding algorithm, by converting the puncturing nodes to regular source nodes and by following the encoding rule at the decoder. The transmitted doping bits in place of punctured bits, with the modified decoding algorithm at the decoder, feed all the punctured nodes with reliable log likelihood ratios. This enables the proposed decoding algorithm to recover all punctured nodes in the early iteration. The fast convergence leads to decoder complexity reduction while providing considerable improvement in performance.

Hybrid Decoding Algorithm for LDPC Codes with Circles

2011 ◽  
Vol 271-273 ◽  
pp. 258-263
Author(s):  
Li Shuang Hu ◽  
Ming Shan Liu ◽  
Yuan Zhou ◽  
Yang Sun
Keyword(s):  
Error Rate ◽  
Belief Propagation ◽  
Additive White Gaussian Noise ◽  
Ldpc Codes ◽  
Error Correcting Codes ◽  
Parity Check ◽  
Likelihood Ratios ◽  
Decoding Algorithms ◽  
Variable Node ◽  
Check Node

At present, Low-Density Parity-Check (LDPC) codes widely used in many fields of communications have the best performance of all the Error Correcting Codes (ECC). This paper mainly studies the decoding algorithms of LDPC. It proposes an improved algorithm which is named Check-Variable nodes Hybrid(CVH) algorithm on the basis of the existing algorithms. The CVH algorithm can reduce the computational complexity during the check-node update while overcome with the correlation between the variable-node news in a code with circles. As well as, comparing with the original algorithms the performance of the new one saves 0.1 and 0.3 dB than Log-likelihood Ratios (LLR) Belief Propagation (BP) and BP - based algorithms under Additive White Gaussian Noise (AWGN) channel when the Bit Error Rate (BER) falls to through the simulation. This point shows that this algorithm can increase the decoding performance and reduce the error rate effectively.

scholarly journals A Survey on Old and New Approximations to the Function ϕ(x) Involved in LDPC Codes Density Evolution Analysis Using a Gaussian Approximation

Information ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 212
Author(s):  
Francesca Vatta ◽  
Alessandro Soranzo ◽  
Massimiliano Comisso ◽  
Giulia Buttazzoni ◽  
Fulvio Babich
Keyword(s):  
Probability Distribution Function ◽  
Iterative Decoding ◽  
Gaussian Approximation ◽  
Ldpc Codes ◽  
Parity Check ◽  
Recurrent Sequence ◽  
Evolution Analysis ◽  
Low Density Parity Check ◽  
Log Likelihood ◽  
Convergence Performance

Low Density Parity Check (LDPC) codes are currently being deeply analyzed through algorithms that require the capability of addressing their iterative decoding convergence performance. Since it has been observed that the probability distribution function of the decoder’s log-likelihood ratio messages is roughly Gaussian, a multiplicity of moderate entanglement strategies to this analysis has been suggested. The first of them was proposed in Chung et al.’s 2001 paper, where the recurrent sequence, characterizing the passage of messages between variable and check nodes, concerns the function ϕ(x), therein specified, and its inverse. In this paper, we review this old approximation to the function ϕ(x), one variant on it obtained in the same period (proposed in Ha et al.’s 2004 paper), and some new ones, recently published in two 2019 papers by Vatta et al. The objective of this review is to analyze the differences among them and their characteristics in terms of accuracy and computational complexity. In particular, the explicitly invertible, not piecewise defined approximation of the function ϕ(x), published in the second of the two abovementioned 2019 papers, is shown to have less relative error in any x than most of the other approximations. Moreover, its use conducts to an important complexity reduction, and allows better Gaussian approximated thresholds to be obtained.

scholarly journals The Decoding Algorithms For Error-Correcting Product Codes Based On Project Geometry Low-Density Parity-Check Codes

2020 ◽  
Vol 12 (3) ◽  
pp. 399-406
Author(s):  
Lev E. Nazarov ◽  
Keyword(s):  
Turbo Codes ◽  
Ldpc Codes ◽  
Parity Check ◽  
Decoding Algorithm ◽  
Signal Noise ◽  
Product Codes ◽  
Decoding Algorithms ◽  
Low Density Parity Check ◽  
Code Constructions ◽  
Parity Check Codes

The focus of this paper is directed towards the investigation of the characteristics of symbol-by-symbol iterative decoding algorithms for error-correcting block product-codes (block turbo-codes) which enable to reliable information transfer at relatively low received signal/noise and provide high power efficiency. Specific feature of investigated product codes is construction with usage of low-density parity-check codes (LDPC) and these code constructions are in the class of LDPC too. According to this fact the considered code constructions have symbol-by-symbol decoding algorithms developed for total class LDPC codes, namely BP (belief propagation) and its modification MIN_SUM_BP. The BP decoding algorithm is iterative and for implementation the signal/noise is required, for implementation of MIN_SUM_BP decoding algorithm the signal/noise is not required. The resulted characteristics of product codes constructed with usage of LDPC based on project geometry (length of code words, information volume, code rate, error performances) are presented in this paper. These component LDPC codes are cyclic and have encoding and decoding algorithms with low complexity implementation. The computer simulations for encoding and iterative symbol-by-symbol decoding algorithms for the number of turbo-codes with different code rate and information volumes are performed. The results of computer simulations have shown that MIN_SUM_BP decoding algorithm is more effective than BP decoding algorithm for channel with additive white gaussian noise concerning error-performances.

Improved BP Decoding Algorithm for LDPC Codes

2013 ◽  
Vol 846-847 ◽  
pp. 925-928
Author(s):  
Li Na Wang ◽  
Xiao Liu
Keyword(s):  
Posterior Probability ◽  
Prior Probability ◽  
Belief Propagation ◽  
Parity Check ◽  
Decoding Algorithm ◽  
Low Density Parity Check ◽  
Detection Criterion ◽  
Process Error ◽  
Check Matrix ◽  
Parity Check Codes

In this paper, an improved belief propagation decoding algorithm was proposed for low density parity check codes. In the proposed decoding process, error bits can be detected once again after hard-decision in the conventional BP decoding algorithm. The detection criterion is based on check matrix characteristics and D-value between prior probability and posterior probability. Simulation results demonstrate the performance of the improved BP decoding algorithm outperform that of the conventional BP decoding algorithm.

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.

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