Summary: Asymptotically Good Codes Correcting Insertions, Deletions, and
Transpositions
Leonard J. Schulman \Lambda David Zuckerman y
Abstract
We present simple, polynomial­time encodable and decodable codes which are asymptotically good for channels
allowing insertions, deletions and transpositions. As a corollary, they achieve exponential error probability
in a stochastic model of insertion­deletion.
Keywords: error correcting codes, insertion, deletion, transposition, edit distance, asymptotically good,
asynchronous communication.
\Lambda College of Computing, Georgia Institute of Technology, Atlanta GA 30332­0280. E­mail: schulman@cc.gatech.edu.
y On leave from the University of Texas at Austin. E­mail: diz@cs.utexas.edu. Supported in part by NSF NYI Grant No.
CCR­9457799, a David and Lucile Packard Fellowship for Science and Engineering, and an Alfred P. Sloan Research Fellowship.
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1 Introduction
In an asynchronous noisy channel, characters of the received message are not definitively identified with
antecedents in the transmitted message. We describe a code which allows for correction of data modified in
the following ways:
A. Insertion and deletion of characters. (Note that this implies also alteration of characters.)
B. Transpositions of blocks of data: a message of the form ABC is transformed into ACB. (Note that this

Source: Abu-Mostafa, Yaser S. - Department of Mechanical Engineering & Computer Science Department, California Institute of Technology

Collections: Computer Technologies and Information Sciences