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Neural Polar Decoders (NPDs) [14] are an advancement in channel coding that combine neural networks (NNs) with polar codes, providing unified decoding for channels with or without memory, without requiring an explicit channel model. They use four neural networks to approximate the functions of polar decoding: the embedding (E) NN, the check ...
For example, in mathematics, the reference direction is usually drawn as a ray from the pole horizontally to the right, and the polar angle increases to positive angles for ccw rotations, whereas in navigation (bearing, heading) the 0°-heading is drawn vertically upwards and the angle increases for cw rotations. The polar angles decrease ...
As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range of 180°, running from 0° to 180°, and does not pose any problem when calculated from an arccosine, but beware for an arctangent.
Examples of block codes are Reed–Solomon codes, Hamming codes, Hadamard codes, Expander codes, Golay codes, Reed–Muller codes and Polar codes. These examples also belong to the class of linear codes, and hence they are called linear block codes. More particularly, these codes are known as algebraic block codes, or cyclic block codes ...
In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are the radial distance r along the line connecting the point to a fixed point called the origin; the polar angle θ between this radial line and a given polar axis; [a] and
In mathematics, two-center bipolar coordinates is a coordinate system based on two coordinates which give distances from two fixed centers and . [1] This system is very useful in some scientific applications (e.g. calculating the electric field of a dipole on a plane). [2] [3]
If two lines a and k pass through a single point Q, then the polar q of Q joins the poles A and K of the lines a and k, respectively. The concepts of a pole and its polar line were advanced in projective geometry. For instance, the polar line can be viewed as the set of projective harmonic conjugates of a given point, the pole, with respect to ...
For example, how many pennies can be packed into a circle on a tabletop, or in 3 dimensions, how many marbles can be packed into a globe. Other considerations enter the choice of a code. For example, hexagon packing into the constraint of a rectangular box will leave empty space at the corners.