String reconciliation with unknown edit distance

We consider the problem of reconciling two remote strings of arbitrary and unknown similarity using minimum communication, which is at the core of some important problems in networking, cryptography, genetic engineering, and even linguistics. Though this problem is efficiently convertible into a set reconciliation instance, for which efficient solutions exist, this conversion may introduce ambiguity in the decoding process, which may require significant communication and computational resources to resolve. We leverage some recent advances in efficient unique decodability of strings to reduce decoding ambiguity, and thus pave the way for a practical implementation of this string reconciler. For certain random strings and in some ideal cases, our approach reconciles two length n strings that differ in α edits (with α not known a priori) using O (α log ²(n)) communication.