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Towards deterministic tree code constructions

Author(s): Braverman, Mark

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Abstract: We present a deterministic operator on tree codes -- we call tree code product -- that allows one to deterministically combine two tree codes into a larger tree code. Moreover, if the original tree codes are efficiently encodable and decodable, then so is their product. This allows us to give the first deterministic subexponential-time construction of explicit tree codes: we are able to construct a tree code T of size n in time 2nε,. Moreover, T is also encodable and decodable in time 2nε,. We then apply our new construction to obtain a deterministic constant-rate error-correcting scheme for interactive computation over a noisy channel with random errors. If the length of the interactive computation is n, the amount of computation required is deterministically bounded by n1+o(1), and the probability of failure is n-ω(1).
Publication Date: 2012
Citation: Braverman, Mark. "Towards deterministic tree code constructions." In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference (2012): pp. 161-167. doi:10.1145/2090236.2090250
DOI: 10.1145/2090236.2090250
Pages: 161 - 167
Type of Material: Conference Article
Journal/Proceeding Title: Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Version: Author's manuscript

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