A Deterministic Polynomial-Time Protocol for Synchronizing From Deletions

In this paper, we consider a synchronization problem between nodes A and B that are connected through a two-way communication channel. Node A contains a binary file X of length n and node B contains a binary file Y that is generated by randomly deleting bits from X, by a small deletion rate β. The location of deleted bits is not known to either node A or node B. We offer a deterministic, polynomial-time synchronization scheme between nodes A and B that needs a total of O(n βlog 1/β) transmitted bits and reconstructs X at node B with probability of error that is exponentially low in the size of X. Orderwise, the rate of our scheme matches the optimal rate for this channel.

[1]  Kannan Ramchandran,et al.  Interactive low-complexity codes for synchronization from deletions and insertions , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[2]  Jack K. Wolf,et al.  Noiseless coding of correlated information sources , 1973, IEEE Trans. Inf. Theory.

[3]  Alexandre V. Evfimievski.  A probabilistic algorithm for updating files over a communication link , 1998, SODA '98.

[4]  Adam Tauman Kalai,et al.  Tight asymptotic bounds for the deletion channel with small deletion probabilities , 2010, 2010 IEEE International Symposium on Information Theory.

[5]  Alon Orlitsky,et al.  Practical protocols for interactive communication , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[6]  Andrew Tridgell,et al.  Efficient Algorithms for Sorting and Synchronization , 1999 .

[7]  Torsten Suel,et al.  Improved file synchronization techniques for maintaining large replicated collections over slow networks , 2004, Proceedings. 20th International Conference on Data Engineering.

[8]  Yashodhan Kanoria,et al.  On the deletion channel with small deletion probability , 2009, 2010 IEEE International Symposium on Information Theory.

[9]  Aaron D. Wyner,et al.  The rate-distortion function for source coding with side information at the decoder , 1976, IEEE Trans. Inf. Theory.

[10]  Alon Orlitsky.  Interactive Communication of Balanced Distributions and of Correlated Files , 1993, SIAM J. Discret. Math..

[11]  Lara Dolecek,et al.  Synchronization from insertions and deletions under a non-binary, non-uniform source , 2013, 2013 IEEE International Symposium on Information Theory.

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

[13]  Rüdiger L. Urbanke,et al.  Efficient encoding of low-density parity-check codes , 2001, IEEE Trans. Inf. Theory.

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

[15]  Michael Mitzenmacher,et al.  A Survey of Results for Deletion Channels and Related Synchronization Channels , 2008, SWAT.

[16]  M. Mitzenmacher.  A survey of results for deletion channels and related synchronization channels , 2009 .

[17]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[18]  Lara Dolecek,et al.  Synchronization from deletions through interactive communication , 2012, 2012 7th International Symposium on Turbo Codes and Iterative Information Processing (ISTC).

[19]  Kannan Ramchandran,et al.  Efficient file synchronization: A distributed source coding approach , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[20]  Chuohao Yeo,et al.  VSYNC: a novel video file synchronization protocol , 2008, ACM Multimedia.

[21]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[22]  Uzi Vishkin,et al.  Communication complexity of document exchange , 1999, SODA '00.