Duplication-Correcting Codes

TL;DR

This paper introduces new code constructions for correcting tandem and palindromic duplications in sequences, compares their redundancies with theoretical bounds, and finds that palindromic duplication correction requires more redundancy.

Contribution

It provides the first constructions for correcting multiple consecutive symbol duplications, including palindromic types, and establishes bounds on their redundancy compared to burst insertions.

Findings

Palindromic duplications require more redundancy than tandem duplications.

Redundancy for correcting these duplications is significantly less than for arbitrary burst insertions.

Upper bounds on code size are derived from sphere packing and tandem deletion bounds.

Abstract

In this work, we propose constructions that correct duplications of multiple consecutive symbols. These errors are known as tandem duplications, where a sequence of symbols is repeated; respectively as palindromic duplications, where a sequence is repeated in reversed order. We compare the redundancies of these constructions with code size upper bounds that are obtained from sphere packing arguments. Proving that an upper bound on the code cardinality for tandem deletions is also an upper bound for inserting tandem duplications, we derive the bounds based on this special tandem deletion error as this results in tighter bounds. Our upper bounds on the cardinality directly imply lower bounds on the redundancy which we compare with the redundancy of the best known construction correcting arbitrary burst insertions. Our results indicate that the correction of palindromic duplications requires more redundancy than the correction of tandem duplications and both significantly less than arbitrary burst insertions.