Coding for Interactive Communication Correcting Insertions and Deletions
Mark Braverman,Ran Gelles,Jieming Mao,Rafail Ostrovsky +3 more
- Vol. 55, pp 14
TLDR
In this paper, the authors considered the problem of interactive communication in which two remote parties perform a computation while their communication channel is (adversarially) noisy, and they obtained the first interactive coding scheme that has a constant rate and tolerates noise rates of up to 1/18 - epsilon.Abstract:
We consider the question of interactive communication, in which two remote parties perform a computation while their communication channel is (adversarially) noisy. We extend here the discussion into a more general and stronger class of noise, namely, we allow the channel to perform insertions and deletions of symbols. These types of errors may bring the parties "out of sync", so that there is no consensus regarding the current round of the protocol.
In this more general noise model, we obtain the first interactive coding scheme that has a constant rate and tolerates noise rates of up to 1/18 - epsilon. To this end we develop a novel primitive we name edit distance tree code. The edit distance tree code is designed to replace the Hamming distance constraints in Schulman's tree codes (STOC 93), with a stronger edit distance requirement. However, the straightforward generalization of tree codes to edit distance does not seem to yield a primitive that suffices for communication in the presence of synchronization problems. Giving the "right" definition of edit distance tree codes is a main conceptual contribution of this work.read more
Citations
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Book
Coding for Interactive Communication: A Survey
TL;DR: Coding for interactive communication as mentioned in this paper augments coding theory to the interactive setting: instead of communicating a message from a sender to a receiver, here the parties are involved in an interacti...
Proceedings ArticleDOI
Synchronization Strings: Codes for Insertions and Deletions Approaching the Singleton Bound
TL;DR: This paper focuses on designing insdel codes, i.e., error correcting block codes (ECCs) for insertion deletion channels, and introduces synchronization strings, which provide a novel way of efficiently dealing with synchronization errors.
Proceedings ArticleDOI
Synchronization strings: codes for insertions and deletions approaching the Singleton bound
TL;DR: In this paper, the authors introduce synchronization strings, which provide a novel way of efficiently dealing with synchronization errors, i.e., insertions and deletions, and construct codes with constant rate, constant distance, and constant alphabet size for insertion deletion channels.
Journal ArticleDOI
Synchronization Strings and Codes for Insertions and Deletions—A Survey
TL;DR: The recent progress in designing efficient error-correcting codes over finite alphabets that can correct a constant fraction of worst-case insertions and deletions is surveyed.
Journal ArticleDOI
Coding for Interactive Communication Correcting Insertions and Deletions
TL;DR: This work develops a novel primitive, carefully designed to replace the Hamming distance constraints in Schulman’s tree codes with a stronger edit-distance requirement, and obtains the first interactive coding scheme that has a constant rate and tolerates noise rates of up to $1/18- \varepsilon $.
References
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Journal ArticleDOI
Asymptotically good codes correcting insertions, deletions, and transpositions
TL;DR: In this paper, the authors present simple, polynomial time encodable and decodable codes which are asymptotically good for channels allowing insertions, deletions, and transpositions.