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en:projects:details:phd04 [2010/09/22 14:12]
mahdi
en:projects:details:phd04 [2010/09/22 14:13]
mahdi
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 Next, we use randomness condensers and extractors to design ensembles of error-correcting codes that achieve the information-theoretic capacity of a large class of communication channels, and then use the obtained ensembles for construction of explicit capacity achieving codes. Finally, we consider the problem of explicit construction of error-correcting codes on the //​Gilbert-Varshamov bound// and extend the original idea of Nisan and Wigderson to obtain a small ensemble of codes, mostly achieving the bound, under suitable computational hardness assumptions. Next, we use randomness condensers and extractors to design ensembles of error-correcting codes that achieve the information-theoretic capacity of a large class of communication channels, and then use the obtained ensembles for construction of explicit capacity achieving codes. Finally, we consider the problem of explicit construction of error-correcting codes on the //​Gilbert-Varshamov bound// and extend the original idea of Nisan and Wigderson to obtain a small ensemble of codes, mostly achieving the bound, under suitable computational hardness assumptions.
  
-\noindent\textit{Keywords: Derandomization theory, randomness +**Keywords:** Derandomization theory, randomness extractors, pseudorandomness,​ wiretap channels, group testing, error-correcting codes. 
-  ​extractors, pseudorandomness,​ wiretap channels, group testing, +
-  ​error-correcting codes.}+