Improved Constructions of Two-Source Extractors

Abstract: In a recent breakthrough \cite{CZ15}, Chattopadhyay and Zuckerman gave an explicit two-source extractor for min-entropy $k \geq \log^C n$ for some large enough constant $C$. However, their extractor only outputs one bit. In this paper, we improve the output of the two-source extractor to $k<sup>{\Omega(1)}$, while the error remains $n<sup>{-\Omega(1)}$. Our improvement is obtained by giving a better extractor for $(q, t, \gamma)$ non-oblivious bit-fixing sources, which can output $t<sup>{\Omega(1)}$ bits instead of one bit as in \cite{CZ15}.