Coding for Interactive Communication Correcting Insertions and Deletions

Braverman, Mark; Gelles, Ran; Mao, Jieming; Ostrovsky, Rafail

doi:10.1109/tit.2017.2734881

Cited by 37 publications

(51 citation statements)

References 34 publications

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“…In this spirit, we suggest the definition of a, to our knowledge, new string distance measure which we call relative suffix distance, which intuitively measures the worst fraction of insdel errors to transform suffixes, i.e., recently sent parts of two strings, into each other. This natural measure, in contrast to a similar measure defined in [2], turns out to induce a metric space on any set of strings.…”

Section: Synchronization Strings: Definition Construction and Decodingmentioning

confidence: 99%

“…To our knowledge, this metric is new. It is, however, similar in spirit to the suffix "distance" defined in [2], which unfortunately is non-symmetric and does not satisfy the triangle inequality but can otherwise be used in a similar manner as RSD in the specific context here (see also Section 6.6).…”

Section: Synchronization Stringsmentioning

confidence: 99%

“…They make progress on the issues raised above and have applications in a large variety of settings and problems. We already found applications to channel simulations, synchronization sequences [21], interactive coding schemes [4-7, 15, 17], edit distance tree codes [2], and error correcting codes for insertion and deletions and suspect there will be many more. In this paper we focus on the last application, namely, designing efficient error correcting block codes over large alphabets for worst-case insertion-deletion channels.The knowledge on efficient error correcting block codes for insertions and deletions, also called insdel codes, severely lacks behind what is known for codes for Hamming errors.…”

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Synchronization strings

Haeupler

Shahrasbi

2017

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

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We introduce synchronization strings, which provide a novel way of efficiently dealing with synchronization errors, i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to deal with than more commonly considered half-errors, i.e., symbol corruptions and erasures. For every ε > 0, synchronization strings allow to index a sequence with an ε −O(1) size alphabet such that one can efficiently transform k synchronization errors into (1 + ε)k half-errors. This powerful new technique has many applications. In this paper, we focus on designing insdel codes, i.e., error correcting block codes (ECCs) for insertion-deletion channels.While ECCs for both half-errors and synchronization errors have been intensely studied, the later has largely resisted progress. As Mitzenmacher puts it in his 2009 survey [22]: "Channels with synchronization errors . . . are simply not adequately understood by current theory. Given the near-complete knowledge we have for channels with erasures and errors ... our lack of understanding about channels with synchronization errors is truly remarkable." Indeed, it took until 1999 for the first insdel codes with constant rate, constant distance, and constant alphabet size to be constructed and only since 2016 are there constructions of constant rate insdel codes for asymptotically large noise rates. Even in the asymptotically large or small noise regime these codes are polynomially far from the optimal rate-distance tradeoff. This makes the understanding of insdel codes up to this work equivalent to what was known for regular ECCs after Forney introduced concatenated codes in his doctoral thesis 50 years ago.A straight forward application of our synchronization strings based indexing method gives a simple black-box construction which transforms any ECC into an equally efficient insdel code with only a small increase in the alphabet size. This instantly transfers much of the highly developed understanding for regular ECCs into the realm of insdel codes. Most notably, for the complete noise spectrum we obtain efficient "near-MDS" insdel codes which get arbitrarily close to the optimal rate-distance tradeoff given by the Singleton bound. In particular, for any δ ∈ (0, 1) and ε > 0 we give insdel codes achieving a rate of 1 − δ − ε over a constant size alphabet that efficiently correct a δ fraction of insertions or deletions.Since the fundamental works of Shannon, Hamming, and others the field of coding theory has advanced our understanding of how to efficiently correct symbol corruptions and erasures. The practical and theoretical impact of error correcting codes on technology and engineering as well as mathematics, theoretical computer science, and other fields is hard to overestimate. The problem of coding for timing errors such as closely related insertion and deletion errors, however, while also studied intensely since the 60s, has largely resisted such progress and impact so far. An expert panel [8] in 1963 concluded: "There has been one glaring hole in [Sh...

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Section: Synchronization Strings: Definition Construction and Decodingmentioning

confidence: 99%

Section: Synchronization Stringsmentioning

confidence: 99%

mentioning

confidence: 99%

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Synchronization strings

Haeupler

Shahrasbi

2017

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

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“…Braverman [4] gave another efficient coding scheme, yet with a slightly reduced success probability. Other related work in the two-party setting considers the case of adversarial noise rather than random noise, in various settings [1,3,5,7,8,10,12,14,18,[22][23][24]; see [16] for a survey.…”

Section: Related Workmentioning

confidence: 99%

Constant-Rate Coding for Multiparty Interactive Communication Is Impossible

Braverman

Efremenko

Gelles

et al. 2017

J. ACM

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We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability ε. We analyze the minimal overhead that must be added by the coding scheme to succeed in performing the computation despite the noise. Our main result is a lower bound on the communication of any noise-resilient protocol over a synchronous star network with n parties (where all parties communicate in every round). Specifically, we show a task that can be solved by communicating T bits over the noise-free network, but for which any protocol with success probability of 1 − o(1) must communicate at least Ω(T log n log log n) bits when the channels are noisy. By a 1994 result of Rajagopalan and Schulman, the slowdown we prove is the highest one can obtain on any topology, up to a log log n factor. We complete our lower bound with a matching coding scheme that achieves the same overhead; thus, the capacity of (synchronous) star networks is Θ(log log n/ log n). Our bounds prove that, despite several previous coding schemes with rate Ω(1) for certain topologies, no coding scheme with constant rate Ω(1) exists for arbitrary n-party noisy networks.

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“…While we focus here on deterministic protocols, ours result also apply to randomized Monte-Carlo protocols. 4 This type of noise, commonly called insertion and deletion noise, is known to be more difficult to deal with in the interactive setting[BGMO16] and may be destructive for asynchronous protocols[FLP85].…”

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confidence: 99%

Making asynchronous distributed computations robust to noise

2018

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We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates any asynchronous distributed protocol while tolerating an optimal corruption of a Θ(1/n) fraction of all messages while incurring a moderate blowup of O(n log 2 n) in the communication complexity.Our result is the first fully distributed interactive coding scheme in which the topology of the communication network is not known in advance. Prior work required either a coordinating node to be connected to all other nodes in the network or assumed a synchronous network in which all nodes already know the complete topology of the network.

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Coding for Interactive Communication Correcting Insertions and Deletions

Cited by 37 publications

References 34 publications

Synchronization strings

Synchronization strings

Constant-Rate Coding for Multiparty Interactive Communication Is Impossible

Making asynchronous distributed computations robust to noise

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