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

1
College of Information Engineering, China Jiliang University, Hangzhou 310018, China
2
Binjiang College, Nanjing University of Information Science & Technology, Wuxi 214105, China
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(5), 457; https://doi.org/10.3390/e21050457
Received: 5 March 2019 / Revised: 26 April 2019 / Accepted: 29 April 2019 / Published: 1 May 2019
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Abstract

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. View Full-Text
Keywords: density evolution; Gaussian approximation; BP algorithm; TDMP algorithm; convergence speed density evolution; Gaussian approximation; BP algorithm; TDMP algorithm; convergence speed
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Wang, X.; Chang, H.; Li, J.; Cao, W.; Shan, L. Analysis of TDMP Algorithm of LDPC Codes Based on Density Evolution and Gaussian Approximation. Entropy 2019, 21, 457.

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