Extractor codes

We study error-correcting codes for highly noisy channels. For example, every received signal in the channel may originate from some half of the symbols in the alphabet. Our main conceptual contribution is an equivalence between error-correcting codes for such channels and extractors. Our main technical contribution is a new explicit error-correcting code based on Trevisan's extractor that can handle such channels, and even noisier ones. Our new code has polynomial-time encoding and polynomial-time soft-decision decoding. We note that Reed?Solomon codes cannot handle such channels, and our study exposes some limitations on list decoding of Reed?Solomon codes. Another advantage of our equivalence is that when the Johnson bound is restated in terms of extractors, it becomes the well-known Leftover Hash Lemma. This yields a new proof of the Johnson bound which applies to large alphabets and soft decoding. Our explicit codes are useful in several applications. First, they yield algori...

• Type: Conference
• Year: 2001
• Where: STOC
• Authors: Amnon Ta-Shma, David Zuckerman
• Keywords: Algorithms, Auxiliary Random Bits, Johnson Bound, STOC 2001, Well-known Leftover Hash