List Decoding and Pseudorandom Constructions
There is a rich interplay between coding theory and computational complexity theory that has enriched both disciplines over the years. In particular, list decoding and closely related notions have been instrumental in several advances in explicit constructions of combinatorial objects with strong “random-like” properties, such as expander graphs, randomness extractors, and pseudorandom generators. Our aim here is to present
a unified list-decoding-centric view of the definition of these objects, and
the details of recent work due to the author, C. Umans, and S. Vadhan , where this viewpoint yields powerful results, namely the construction of unbalanced bipartite graphs with very strong expansion properties based on the list-decodable codes due to Parvaresh and Vardy . In turn these expanders yield simple constructions of randomness extractors that are optimal up to constant factors.
Unable to display preview. Download preview PDF.
- 1.Guruswami, V.: Better Extractors for Better Codes? In: 36th Annual ACM Symposium on Theory of Computing, pp. 436–444 (2004)Google Scholar
- 2.Guruswami, V., Rudra, A.: Explicit Capacity-Achieving List-Decodable Codes. In: 38th Annual ACM Symposium on Theory of Computing, pp. 1–10 (2006)Google Scholar
- 3.Guruswami, V., Umans, C., Vadhan, S.: Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes. In: 22nd IEEE Conference on Computational Complexity, pp. 96–108 (2007)Google Scholar
- 4.Parvaresh, F., Vardy, A.: Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time. In: 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 285–294 (2005)Google Scholar
- 7.Ta-Shma, A., Zuckerman, D., Safra, S.: Extractors from Reed-Muller codes. In: 42nd Annual Symposium on Foundations of Computer Science, pp. 638–647 (2001)Google Scholar