منابع مشابه
An information - theoretic proof of Hadamard's inequality
only linearly and not exponentially with the source block length. Since a trellis approaches a tree as the constraint length grows large, this work also suggests an alternate tree coding scheme and proof of the tree coding theorem of Jakatdar and Pearlman [6]. APPENDIX A The generalized Gallager function Edk(p) is defined in (21). In the following we prove that given RN,* > RN-*(De) for allj an...
متن کاملAn information-theoretic proof of Nash's inequality
We show that an information-theoretic property of Shannon's entropy power, known as concavity of entropy power [7], can be fruitfully employed to prove inequalities in sharp form. In particular, the concavity of entropy power implies the logarithmic Sobolev inequality, and the Nash's inequality with the sharp constant.
متن کاملAn Entropic Proof of Chang's Inequality
Chang’s lemma is a useful tool in additive combinatorics and the analysis of Boolean functions. Here we give an elementary proof using entropy. The constant we obtain is tight, and we give a slight improvement in the case where the variables are highly biased. 1 The lemma For S ∈ {0, 1}, let χk : {±1} n → R denote the character χS(x) = ∏ i∈S xi . For any function f : {±1} → R, we can then defin...
متن کاملA new simple proof for an inequality of Cebyshev type
We give here a simple proof of a well-known integral version of Cebyshev inequality. Using the same method, we give a lower bound in the case of increasing functions and then in the case of convex functions. We also establish a result at limit which shows that the constant 1/12 is sharp, in the sense that it cannot be replaced by a smaller one. Subject Classification: 26D15. It is mentioned in ...
متن کاملAn Alternative Proof of an Extremal Entropy Inequality
This paper first focuses on deriving an alternative approach for proving an extremal entropy inequality (EEI), originally presented in [11]. The proposed approach does not rely on the channel enhancement technique, and has the advantage that it yields an explicit description of the optimal solution as opposed to the implicit approach of [11]. Compared with the proofs in [11], the proposed alter...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 2002
ISSN: 0386-2194
DOI: 10.3792/pjaa.78.26