October 4: Leonard J. Schulman (Caltech)

Title: Explicit Binary Tree Codes with Polylogarithmic Size Alphabet

Abstract:

Tree codes are “real time” or “causal” error-correcting codes. They are

known to exist but explicit construction has been a longstanding open

problem. We report on progress on this problem.

For every constant delta we give an explicit binary tree code with

distance delta and alphabet size poly(log n), where n is the depth of

the tree. This is the first improvement over a two-decade-old

construction that has an exponentially larger alphabet of size poly(n).

As part of the analysis, we prove a bound on the number of positive

integer roots a real polynomial can have in terms of its sparsity with

respect to the Newton basis–a result of independent interest.

Joint work with Gil Cohen (Princeton) and Bernhard Haeupler (CMU)