Mark Braverman

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 ... more >>>

Matthew Franklin, Ran Gelles, Rafail Ostrovsky, Leonard Schulman

Error correction and message authentication are well studied in the literature, and various efficient solutions have been suggested and analyzed. This is however not the case for data streams in which the message is very long, possibly infinite, and not known in advance to the sender. Trivial solutions for error-correcting ... more >>>

Alexander A. Sherstov, Pei Wu

Interactive coding, pioneered by Schulman (FOCS 1992, STOC 1993), is concerned with making communication protocols resilient to adversarial noise. The canonical model allows the adversary to alter a small constant fraction of symbols, chosen at the adversary's discretion, as they pass through the communication channel. Braverman, Gelles, Mao, and Ostrovsky ... more >>>

Gil Cohen, Bernhard Haeupler, Leonard Schulman

This paper makes progress on the problem of explicitly constructing a binary tree code with constant distance and constant alphabet size.

For every constant $\delta < 1$ we give an explicit binary tree code with distance $\delta$ and alphabet size $(\log{n})^{O(1)}$, where $n$ is the depth of the tree. This ... more >>>

Gil Cohen, Shahar Samocha

We devise a deterministic interactive coding scheme with rate $1-O(\sqrt{\varepsilon\log(1/\varepsilon)})$ against $\varepsilon$-fraction of adversarial errors. The rate we obtain is tight by a result of Kol and Raz (STOC 2013). Prior to this work, deterministic coding schemes for any constant fraction $\varepsilon>0$ of adversarial errors could obtain rate no larger ... more >>>