Strongly Typical Sequences (strong Typicality, Letter Typicality)
If a sequence x1, ..., xn is drawn from some specified joint distribution defined over a finite or an infinite alphabet, then the strongly typical set, Aε,strong(n) is defined as the set of sequences which satisfy
where is the number of occurrences of a specific symbol in the sequence.
It can be shown that strongly typical sequences are also weakly typical (with a different constant ε), and hence the name. The two forms, however, are not equivalent. Strong typicality is often easier to work with in proving theorems for memoryless channels. However, as is apparent from the definition, this form of typicality is only defined for random variables having finite support.
Read more about this topic: Typical Set
Famous quotes containing the words strongly, typical and/or letter:
“There are some women ... in whom conscience is so strongly developed that it leaves little room for anything else. Love is scarcely felt before duty rushes to encase it, anger impossible because one must always be calm and see both sides, pity evaporates in expedients, even grief is felt as a sort of bruised sense of injury, a resentment that one should have grief forced upon one when one has always acted for the best.”
—Sylvia Townsend Warner (1893–1978)
“The books may say that nine-month-olds crawl, say their first words, and are afraid of strangers. Your exuberantly concrete and special nine-month-old hasn’t read them. She may be walking already, not saying a word and smiling gleefully at every stranger she sees. . . . You can support her best by helping her learn what she’s trying to learn, not what the books say a typical child ought to be learning.”
—Amy Laura Dombro (20th century)
“‘Tis the curse of service,
Preferment goes by letter and affection,
And not by old gradation, where each second
Stood heir to th’ first.”
—William Shakespeare (1564–1616)