Klim Efremenko (Tel Aviv University)
Wednesday, 23.4.2014, 12:30
In this talk we extend the notion of list decoding to the setting of interactive communication and study its limits. In particular, we show that any protocol can be encoded, with a constant rate, into a list-decodable protocol which is resilient to a noise rate of up to $1/2-\varepsilon$, and that this is tight.
Using our list-decodable construction, we study a more nuanced model of noise where the adversary can corrupt up-to $\alpha$ fraction of Alice's communication and up-to $\beta$ fraction of Bob's communication. We will show how to use list-decoding in order to fully characterize the region $R$ of pairs $(\alpha, \beta)$ for which unique decoding with constant rate is possible. The region $R_U$ turns out to be quite unusual in its shape. In particular, it is bounded by a piecewise-differentiable curve with infinitely many pieces.
Joint work with Mark Braverman.