Locally decodable codes (LDCs) are error-correcting codes $C : \Sigma^k \to \Sigma^n$ that admit a local decoding algorithm that recovers each individual bit of the message by querying only a few bits from a noisy codeword. An important question in this line of research is to understand the optimal trade-off ... more >>>

Tree codes are combinatorial structures introduced by Schulman (STOC 1993) as key ingredients in interactive coding schemes. Asymptotically-good tree codes are long known to exist, yet their explicit construction remains a notoriously hard open problem. Even proposing a plausible construction, without the burden of proof, is difficult and the defining ... more >>>

We study the problem of testing discrete distributions with a focus on the high probability regime.
Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and
parameters $0< \epsilon, \delta <1$, we want to distinguish {\em with probability at least $1-\delta$}
whether these distributions satisfy $\mathcal{P}$ ... more >>>