Formal Statement
Let each source symbol from the alphabet
be encoded into a uniquely decodable code over an alphabet of size with codeword lengths
Then
Conversely, for a given set of natural numbers satisfying the above inequality, there exists a uniquely decodable code over an alphabet of size with those codeword lengths.
A commonly occurring special case of a uniquely decodable code is a prefix code. Kraft's inequality therefore also holds for any prefix code.
Read more about this topic: Kraft's Inequality
Famous quotes containing the words formal and/or statement:
“Two clergymen disputing whether ordination would be valid without the imposition of both hands, the more formal one said, “Do you think the Holy Dove could fly down with only one wing?””
—Horace Walpole (1717–1797)
“The parent is the strongest statement that the child hears regarding what it means to be alive and real. More than what we say or do, the way we are expresses what we think it means to be alive. So the articulate parent is less a telling than a listening individual.”
—Polly Berrien Berends (20th century)