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The memorylessness property asserts that the number of previously failed trials has no effect on the number of future trials needed for a success. Geometric random variables can also be defined as taking values in N 0 {\displaystyle \mathbb {N} _{0}} , which describes the number of failed trials before the first success in a sequence of ...
The SC field has the number of caches that share the block. Each cache entry has pointers to the next sharing caches known as L-CHD and R-CHD. A condition for this directory is that the binary tree should be number balanced, i.e the number of nodes in the left sub tree must be equal to or one greater than the number of nodes in the right subtree.
(This formula is sometimes called the Hartley function.) This is the maximum possible rate of information that can be transmitted with that alphabet. (The logarithm should be taken to a base appropriate for the unit of measurement in use.) The absolute rate is equal to the actual rate if the source is memoryless and has a uniform distribution.
A discrete memoryless single-relay channel can be modelled as four finite sets, ,,, and , and a conditional probability distribution (, |,) on these sets. The probability distribution of the choice of symbols selected by the encoder and the relay encoder is represented by p ( x 1 , x 2 ) {\displaystyle p(x_{1},x_{2})} .
Therefore a reverse channel to request re-transmission may not be needed. The cost is a fixed, higher forward channel bandwidth. The cost is a fixed, higher forward channel bandwidth. The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code .
The mathematical model consists of a transition probability that specifies an output distribution for each possible sequence of channel inputs. In information theory, it is common to start with memoryless channels in which the output probability distribution only depends on the current channel input. A channel model may either be digital or analog.
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A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present values) depends only upon the present state; that is, given the present, the future does not depend on the past.