IEEE Transactions on Information Theory - Part 1
Coding for interactive communication
IEEE Transactions on Information Theory - Part 1
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Tree codes and a conjecture on exponential sums
Proceedings of the 5th conference on Innovations in theoretical computer science
| Hi-index | 0.00 |
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).