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If Kraft's inequality holds with strict inequality, the code has some redundancy. If Kraft's inequality holds with equality, the code in question is a complete code. [2] If Kraft's inequality does not hold, the code is not uniquely decodable. For every uniquely decodable code, there exists a prefix code with the same length distribution.
A useful theorem in additive combinatorics is Plünnecke–Ruzsa inequality. This theorem gives an upper bound on the cardinality of | nA − mA | in terms of the doubling constant of A. For instance using Plünnecke–Ruzsa inequality, we are able to prove a version of Freiman's Theorem in finite fields.
In mathematics, the following inequality is known as Titu's lemma, Bergström's inequality, Engel's form or Sedrakyan's inequality, respectively, referring to the article About the applications of one useful inequality of Nairi Sedrakyan published in 1997, [1] to the book Problem-solving strategies of Arthur Engel published in 1998 and to the book Mathematical Olympiad Treasures of Titu ...
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution
A great many important inequalities in information theory are actually lower bounds for the Kullback–Leibler divergence.Even the Shannon-type inequalities can be considered part of this category, since the interaction information can be expressed as the Kullback–Leibler divergence of the joint distribution with respect to the product of the marginals, and thus these inequalities can be ...
We'll cover exactly how to play Strands, hints for today's spangram and all of the answers for Strands #283 on Wednesday, December 11. ... 300 Trivia Questions and Answers to Jumpstart Your Fun ...
The College Football Playoff got underway Friday but the main course is spread out through Saturday. Three first-round games will be played across three separate campus sites from State College ...
There are three inequalities between means to prove. There are various methods to prove the inequalities, including mathematical induction, the Cauchy–Schwarz inequality, Lagrange multipliers, and Jensen's inequality. For several proofs that GM ≤ AM, see Inequality of arithmetic and geometric means.