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Tanner proved the following bounds Let be the rate of the resulting linear code, let the degree of the digit nodes be and the degree of the subcode nodes be .If each subcode node is associated with a linear code (n,k) with rate r = k/n, then the rate of the code is bounded by
Repetition codes are one of the few known codes whose code rate can be automatically adjusted to varying channel capacity, by sending more or less parity information as required to overcome the channel noise, and it is the only such code known for non-erasure channels.
Subtracting from both sides and dividing by 2 by two yields the power-reduction formula for sine: = ( ()). The half-angle formula for sine can be obtained by replacing θ {\displaystyle \theta } with θ / 2 {\displaystyle \theta /2} and taking the square-root of both sides: sin ( θ / 2 ) = ± ( 1 − cos θ ) / 2 ...
Related: 16 Games Like Wordle To Give You Your Word Game Fix More Than Once Every 24 Hours We'll have the answer below this friendly reminder of how to play the game .
The U.S. Food and Drug Administration (FDA) now classifies eggs as a “healthy, nutrient-dense" food, according to a new proposed rule. Registered dietitians react to the change.
Discount grocery store Aldi is expanding and will soon have new locations in nine states. Seventeen new Aldi stores are preparing for grand openings, per the Aldi website. Most of the locations ...
A function with period P will repeat on intervals of length P, and these intervals are sometimes also referred to as periods of the function. Geometrically, a periodic function can be defined as a function whose graph exhibits translational symmetry , i.e. a function f is periodic with period P if the graph of f is invariant under translation ...
In coding theory, an expander code is a [,] linear block code whose parity check matrix is the adjacency matrix of a bipartite expander graph.These codes have good relative distance (), where and are properties of the expander graph as defined later, rate (), and decodability (algorithms of running time () exist).