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Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
Forward-Backward Euler method The result of applying both the Forward Euler method and the Forward-Backward Euler method for a = 5 {\displaystyle a=5} and n = 30 {\displaystyle n=30} . In order to apply the IMEX-scheme, consider a slightly different differential equation:
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta ...
This differs from the (forward) Euler method in that the forward method uses (,) in place of (+, +). The backward Euler method is an implicit method: the new approximation y k + 1 {\displaystyle y_{k+1}} appears on both sides of the equation, and thus the method needs to solve an algebraic equation for the unknown y k + 1 {\displaystyle y_{k+1}} .
This is the Euler method (or forward Euler method, in contrast with the backward Euler method, to be described below). The method is named after Leonhard Euler who described it in 1768. The Euler method is an example of an explicit method. This means that the new value y n+1 is defined in terms of things that are already known, like y n.
The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected.
Error-correcting codes are used in lower-layer communication such as cellular network, high-speed fiber-optic communication and Wi-Fi, [11] [12] as well as for reliable storage in media such as flash memory, hard disk and RAM. [13] Error-correcting codes are usually distinguished between convolutional codes and block codes:
[c] Essentially, backpropagation evaluates the expression for the derivative of the cost function as a product of derivatives between each layer from right to left – "backwards" – with the gradient of the weights between each layer being a simple modification of the partial products (the "backwards propagated error").