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Studies in computational intelligence

A Closer Look at the Modeling of Economics Data

Hung T. Nguyen, Nguyễn Ngọc Thạch

Published Nov 23, 2018• 16 citations
Publisher
DOI
10.1007/978-3-030-04200-4_7

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Low density parity-check code (LDPC) is an error correcting code used in noisy communication channel (e.g. AWGN) to reduce the probability of error in information. By using LDPC codes, this probability can be made comparatively small, so that the data transmission rate can be as close to Shannon's limit. The decoding of Low Density Parity Check (LDPC) codes by iterative process of belief propagation gives challenges for designers looking for real time performance in communication systems. This thesis work proposes the use of Artificial Neural Networks (ANN) to replace belief propagation to approach closer to Shannon's limit more closer than other traditional decoding methods. This thesis is intended to design a new methodology to decode LDPC codes in Non-iterative manner with the help of ANN and Look Up Table (LUT). This work is at initial stage and will be extended for better performance.
We make use of the calculation of Achiam and Kosterlitz and investigate the generalization of the Migdal-type renormalization-group calculation to critical dynamics, by looking at the one- and two-dimensional kinetic Ising model with no conserved magnetization. In the two-dimensional case the dynamical critical index ZM(magneticperturbation)=2.064{Z}_{M}(\mathrm{magnetic}\mathrm{perturbation})=2.064ZM​(magneticperturbation)=2.064 and ZE(energylikeperturbation)=1.819{Z}_{E}(\mathrm{energylike}\mathrm{perturbation})=1.819ZE​(energylikeperturbation)=1.819 for scale factor $\ensuremath{\lambda}=1$. ZM{Z}_{M}ZM​ involves the static $\frac{\ensuremath{\beta}}{\ensuremath{\nu}}$ exponent, while ZE{Z}_{E}ZE​ involves $\frac{1}{\ensuremath{\nu}}$, and therefore, it is not surprising that ZM{Z}_{M}ZM​ is closer to the high-temperature expansion results, since $\frac{\ensuremath{\beta}}{\ensuremath{\nu}}$ in the Migdal approximation for statics is much closer to the exact value than $\frac{1}{\ensuremath{\nu}}$. In one dimension we obtain ZM=ZE=2{Z}_{M}={Z}_{E}=2ZM​=ZE​=2, which is the exact result of Glauber.