8. For what values of a and b is g(x) = \left\{\begin{matrix} ax+2b, &x\leq 0\x^2+3a-b,&0<x\leq2\3x-5,& x>2 \end{matrix}\right. If z^3-xz-y=0, prove that \partial^2 z dx dy =-3z^2+x (3z^2-x)^3 . Use the ratio t
Matrix:The rank of a matrix which is the array arrangement of rows and columns is given by the maximum number of independent rows/columns it posses. If the rows and columns are not the same in number then the rank is calculated by the linearly independent test applied upon the one with ...
Two vectors of Zpn are orthogonal if their scalar product is zero, the scalar product of two vectors being calculated using the rules of the algebra modulo p. If C has n as length and k as dimension, every parity check matrix H of C must have n rows and n − k columns and H ...
Near Shannon limit performance of low density parity check codes
a Sound waveforms of a bassoon and a clarinet (left) were linearly transformed to two mixed signals (right). The diagonal and off-diagonal elements of the mixing matrix were 1 and 0.5, respectively. b Nonstationary Poisson spike trains of 200 input neurons (from a total of 500) are shown...
monkey checks when the gauge is full. It is noteworthy that if the gauge becomes full it remains full until the monkey checks the bonus option. Good performance in the main task increases the level of the gauge, bringing the bonus closer to delivery. Specifically, the number of correct ...
matrix H. The r ×1 vector s = H· c T is denoted as the “syndrome” of c through H. Hence, c belongs to C if and only if its syndrome through H is null. Any r linearly independent vectors in Γ ⊥ can be used to forma valid parity-check matrix, so H is not unique for ...
How to tell if the matrix has eigenvalue 0? Let B=\begin{bmatrix} 1 & -2 & 0 & 4\\ 1 & 2 & 3 & -3\\ -1 & 1 & 4 & -1\\ 2 & 0 & 1 & 0 \end{bmatrix}, Determine whether each vector is an eigenvector of B: a) \begin{bmatrix} -1\\ 0\\ 0\\ 1 \e ...
matrix for processing in the LDPC decoder immediately after the first set of rows, each of the rows of the second plurality of rows is datawise independent of each of the rows of the first plurality of rows; wherein the LDPC matrix comprises a plurality of layers and at least one row in...
matrix, wherein the first block is dependent on a result of the most recently processed layer that is unavailable at a time that the first block is being processed, wherein the circuitry comprises an array of final state register banks, each bank comprising a plurality of registers for ...