Reliable communication over channels with insertions, deletions, and substitutions

A new block code is introduced which is capable of correcting multiple insertion, deletion, and substitution errors. The code consists of nonlinear inner codes, which we call "watermark"" codes, concatenated with low-density parity-check codes over nonbinary fields. The inner code allows probabilistic resynchronization and provides soft outputs for the outer decoder, which then completes decoding. We present codes of rate 0.7 and transmitted length 5000 bits that can correct 30 insertion/deletion errors per block. We also present codes of rate 3/14 and length 4600 bits that can correct 450 insertion/deletion errors per block.

[1]  Jack J. Stiffler,et al.  Comma-free error-correcting codes , 1965, IEEE Trans. Inf. Theory.

[2]  T. R. Hatcher.  On a family of error-correcting and synchronizable codes (Corresp.) , 1969, IEEE Trans. Inf. Theory.

[3]  D. Mackay,et al.  Evaluation of Gallager Codes for Short Block Length and High Rate Applications , 2001 .

[4]  David J. C. MacKay,et al.  Good Error-Correcting Codes Based on Very Sparse Matrices , 1997, IEEE Trans. Inf. Theory.

[5]  I. M. Jacobs,et al.  Principles of Communication Engineering , 1965 .

[6]  Jeffrey D. Ullman,et al.  On the capabilities of codes to correct synchronization errors , 1967, IEEE Trans. Inf. Theory.

[7]  David J. C. MacKay,et al.  Low-density parity check codes over GF(q) , 1998, IEEE Communications Letters.

[8]  David Sankoff,et al.  Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison , 1983 .

[9]  Michael S. Waterman,et al.  Introduction to computational biology , 1995 .

[10]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[11]  Rüdiger L. Urbanke,et al.  The capacity of low-density parity-check codes under message-passing decoding , 2001, IEEE Trans. Inf. Theory.

[12]  T. Hatcher.  ON A FAMILY OF ERROR CORRECTING AND SYNCHRONIZABLE CODES. , 1974 .

[13]  Frederick F. Sellers,et al.  Bit loss and gain correction code , 1962, IRE Trans. Inf. Theory.

[14]  David L. Neuhoff,et al.  Codes for data synchronization and timing , 1999, Proceedings of the 1999 IEEE Information Theory and Communications Workshop (Cat. No. 99EX253).

[15]  Karen Kukich,et al.  Techniques for automatically correcting words in text , 1992, CSUR.

[16]  Stafford E. Tavares,et al.  Matrix approach to synchronization recovery for binary cyclic codes , 1969, IEEE Trans. Inf. Theory.

[17]  D. Mackay,et al.  Low-Density Parity Check Codes over , 1998 .

[18]  Lorenzo Calabi,et al.  A family of codes for the correction of substitution and synchronization errors , 1969, IEEE Trans. Inf. Theory.

[19]  Vladimir I. Levenshtein,et al.  Binary codes capable of correcting deletions, insertions, and reversals , 1965 .

[20]  R. Gallager.  SEQUENTIAL DECODING FOR BINARY CHANNELS WITH NOISE AND SYNCHRONIZATION ERRORS , 1961 .

[21]  G. Tenengolts,et al.  Nonbinary codes, correcting single deletion or insertion , 1984, IEEE Trans. Inf. Theory.

[22]  David Zuckerman,et al.  Asymptotically good codes correcting insertions, deletions, and transpositions , 1997, SODA '97.

[23]  F H Crick,et al.  CODES WITHOUT COMMAS. , 1957, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Harold Marston Morse.  Recurrent geodesics on a surface of negative curvature , 1921 .

[25]  Frederick Jelinek,et al.  Statistical methods for speech recognition , 1997 .

[26]  S. Golomb,et al.  Comma-Free Codes , 1958, Canadian Journal of Mathematics.

[27]  Eiichi Tanaka,et al.  Synchronization and substitution error-correcting codes for the Levenshtein metric , 1976, IEEE Trans. Inf. Theory.

[28]  Patrick A. V. Hall,et al.  Approximate String Matching , 1994, Encyclopedia of Algorithms.