A short note on the joint entropy of n/2-wise independence
نویسندگان
چکیده
In this note, we prove a tight lower bound on the joint entropy of n unbiased Bernoulli random variables which are n/2-wise independent. For general k-wise independence, we give new lower bounds by adapting Navon and Samorodnitsky’s Fourier proof of the ‘LP bound’ on error correcting codes. This counts as partial progress on a problem asked by Gavinsky and Pudlák in [3].
منابع مشابه
Entropy Versus Pairwise Independence
We give lower bounds on the joint entropy of n pairwise independent random variables. We show that if the variables have no dominant value (their min-entropies are bounded away from zero) then this joint entropy grows as Ω(log n). This rate of growth is known to be best possible. If k-wise independence is assumed, we obtain an optimal Ω(k log n) lower bound for not too large k. We also show tha...
متن کاملA note on inequalities for Tsallis relative operator entropy
In this short note, we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy, {em Math. Inequal. Appl.} {18} (2015), no. 2, 401--406]. Meanwhile, we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...
متن کاملOn the Joint Entropy of $d$-Wise-Independent Variables
How low can be the joint entropy of n d-wise independent (for d ≥ 2) discrete random variables? This question has been posed and partially answered in a recent work of Babai [Bab13]. In this paper we improve some of his bounds, prove new bounds in a wider range of parameters and show matching upper bounds in some special cases. In particular, we prove tight lower bounds for the min-entropy (as ...
متن کاملa Comparison Study Between the Joint Probability Approach and Time Series Rainfall Modelling in Coastal Detention Pond Analysis (RESEARCH NOTE)
In tidally affected coastal catchments detention pond should be provided to store flood surface water. A comparison between the full simulation approach based on the joint probability method and time series rainfall modeling via the annual maximum of pond level was undertaken to investigate the assumptions of independence between variables that are necessary in the joint probability method. The...
متن کاملISAR Image Improvement Using STFT Kernel Width Optimization Based On Minimum Entropy Criterion
Nowadays, Radar systems have many applications and radar imaging is one of the most important of these applications. Inverse Synthetic Aperture Radar (ISAR) is used to form an image from moving targets. Conventional methods use Fourier transform to retrieve Doppler information. However, because of maneuvering of the target, the Doppler spectrum becomes time-varying and the image is blurred. Joi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1709.00752 شماره
صفحات -
تاریخ انتشار 2017