Fourier Analysis of Linear Extractors

Extracting from bit streams remains an active research area in modern cryptography. Recently, there has been renewed interest in debasing with structured linear mappings, namely by linear codes. Linear codes were proposed as extractors for independent but biased bits in the theory community . Decades later, they were popularized among the hardware designers , and …

On Schur-Concavity of Poisson-Binomial

For many problems in mathematics and theoretical computer science, it is of interest to estimate concentration of sums of heterogenous boolean random variables. This note shows some new results obtained through majorization theory with computer-aided proof in SymPy. Results The Poisson Binomial distribution is defined for as$$Y = \sum_{i=1}^n X_i,\quad X_i \sim \mathrm{Bern}(p_i).$$ We are …