scholarly journals New explicitly invertible approximation of the function involved in LDPC codes density evolution analysis using a Gaussian approximation

2019 ◽  
Vol 55 (22) ◽  
pp. 1183-1186 ◽  
Author(s):  
F. Vatta ◽  
A. Soranzo ◽  
M. Comisso ◽  
G. Buttazzoni ◽  
F. Babich
Keyword(s):  
Gaussian Approximation ◽  
Ldpc Codes ◽  
Density Evolution ◽  
Evolution Analysis

scholarly journals Analysis of TDMP Algorithm of LDPC Codes Based on Density Evolution and Gaussian Approximation

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 457 ◽  
Author(s):  
Xiumin Wang ◽  
Hong Chang ◽  
Jun Li ◽  
Weilin Cao ◽  
Liang Shan
Keyword(s):  
Message Passing ◽  
Belief Propagation ◽  
Gaussian Approximation ◽  
Bp Algorithm ◽  
Turbo Decoding ◽  
Density Evolution ◽  
Analysis Process ◽  
Evolution Analysis ◽  
Simplified Algorithm ◽  
Previous Iteration

Based on density evolution analysis of the existing belief propagation (BP) algorithm, the Turbo Decoding Message Passing (TDMP) algorithm was analyzed from the perspective of density evolution and Gaussian approximation, and the theoretical analysis process of TDMP algorithm was given. When calculating the prior message of each layer of the TDMP algorithm, the check message of the previous iteration should be subtracted. Therefore, the result will not be convergent, if the TDMP algorithm is directly analyzed based on density evolution and Gaussian approximation. We researched the TDMP algorithm based on the symmetry conditions to obtain the convergent result. When using density evolution (DE) and Gaussian approximation to analyze the decoding convergence of the TDMP algorithm, we can provide a theoretical basis for proving the superiority of the algorithm. Then, based on the DE theory, we calculated the probability density function (PDF) of the check-to-variable information of TDMP and its simplified algorithm, and then gave it a calculation based on the process of the normalization factor. Simulation results show that the decoding convergence speed of the TDMP algorithm was faster and the iterations were smaller compared to the BP algorithm under the same conditions.

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 Quaternary Message Passing Decoding of LDPC Codes: Density Evolution Analysis and Error Floor

2021 ◽  
Author(s):  
Emna Ben Yacoub ◽  
Balazs Matuz ◽  
Alexandre Graell i Amat ◽  
Gianluigi Liva
Keyword(s):  
Message Passing ◽  
Ldpc Codes ◽  
Error Floor ◽  
Density Evolution ◽  
Evolution Analysis
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