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An indel refers to a single insertion or deletion, while an edit refers to asingle insertion, deletion or substitution. In this paper, we investigate codesthat combat either a single indel or a single edit and provide linear-timealgorithms that encode binary messages into these codes of length n. Over thequaternary alphabet, we provide two linear-time encoders. One corrects a singleedit with log n + O(log log n) redundancy bits, while the other corrects asingle indel with log n + 2 redundant bits. These two encoders areorder-optimal. The former encoder is the first known order-optimal encoder thatcorrects a single edit, while the latter encoder (that corrects a single indel)reduces the redundancy of the best known encoder of Tenengolts (1984) by atleast four bits. Over the DNA alphabet, we impose an additional constraint: theGC-balanced constraint and require that exactly half of the symbols of any DNAcodeword to be either C or G. In particular, via a modification of Knuth'sbalancing technique, we provide a linear-time map that translates binarymessages into GC-balanced codewords and the resulting codebook is able tocorrect a single indel or a single edit. These are the first knownconstructions of GC-balanced codes that correct a single indel or a singleedit.

Optimal Codes Correcting a Single Indel / Edit for DNA-Based Data Storage