Efficient and Explicit Coding for Interactive Communication

Gelles, Ran; Moitra, Ankur; Sahai, Amit

doi:10.1109/focs.2011.51

Cited by 61 publications

(50 citation statements)

References 16 publications

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“…The problem of designing error resilient interactive communication protocols (as opposed to messages) was first studied by Schulman [Sch93], with extensions by [BR11,Bra12,GMS11]. However, in the current paper, we do not require the more complicated ideas of these works, because it turns out that we can obtain our results using simpler protocols that are enough for the error model we consider.…”

Section: Techniquesmentioning

confidence: 75%

Formulas Resilient to Short-Circuit Errors

Kalai

Lewko

Rao

2012

2012 IEEE 53rd Annual Symposium on Foundations of Computer Science

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We show how to efficiently convert any boolean formula F into a boolean formula E that is resilient to short-circuit errors (as introduced by Kleitman et al. [KLM94]). A gate has a short-circuit error when the value it computes is replaced by the value of one of its inputs.We guarantee that E computes the same function as F , as long as at most (1/10 − ε) of the gates on each path from the output to an input have been corrupted in E. The corruptions may be chosen adversarially, and may depend on the formula E and even on the input. We obtain our result by extending the Karchmer-Wigderson connection between formulas and communication protocols to the setting of adversarial error. This enables us to obtain error-resilient formulas from error-resilient communication protocols.

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Section: Techniquesmentioning

confidence: 75%

Formulas Resilient to Short-Circuit Errors

Kalai

Lewko

Rao

2012

2012 IEEE 53rd Annual Symposium on Foundations of Computer Science

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“…We also show that for higher noise rates, no constant-rate interactive protocol exists for tasks that depend on inputs of both parties. Similarly to previous results for interactive communication with adversarial noise [24,5,9], our decoding scheme is inefficient. Very recently, Brakerski and Kalai [2] showed how to augment previous results of interactive communication protocols and achieved efficient schemes that withstand adversarial noise (the computation efficiency was further improved by Brakerski and Naor [3] to O (N log N )).…”

Section: Our Resultsmentioning

confidence: 78%

“…gives a sub-exponential (in N ) construction of a tree code, and Gelles, Moitra and Sahai [9] provide an efficient construction of a randomized relaxation of a tree code of depth N , namely a potent tree code, which is powerful enough as a substitute for a tree code in most applications.…”

Section: For Any Two Paths (Strings) X Y ∈ [D]mentioning

confidence: 99%

Optimal Coding for Streaming Authentication and Interactive Communication

Franklin

Gelles

Ostrovsky

et al. 2013

Advances in Cryptology – CRYPTO 2013

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Abstract. Error correction and message authentication are well studied in the literature, and various efficient solutions have been suggested and analyzed. This is however not the case for data streams in which the message is very long, possibly infinite, and not known in advance to the sender. Trivial solutions for error-correcting and authenticating data streams either suffer from a long delay at the receiver's end or cannot perform well when the communication channel is noisy.In this work we suggest a constant-rate error-correction scheme and an efficient authentication scheme for data streams over a noisy channel (one-way communication, no feedback) in the shared-randomness model. Our first scheme does not assume shared randomness and (nonefficiently) recovers a (1 − 2c)-fraction prefix of the stream sent so far, assuming the noise level is at most c < 1/2. The length of the recovered prefix is tight.To be able to overcome the c = 1/2 barrier we relax the model and assume the parties pre-share a secret key. Under this assumption we show that for any given noise rate c < 1, there exists a scheme that correctly decodes a (1 − c)-fraction of the stream sent so far with high probability, and moreover, the scheme is efficient. Furthermore, if the noise rate exceeds c, the scheme aborts with high probability. We also show that no constant-rate authentication scheme recovers more than a (1 − c)-fraction of the stream sent so far with non-negligible probability, Optimal Coding for Streaming Authentication 259 thus the relation between the noise rate and recoverable fraction of the stream is tight, and our scheme is optimal.Our techniques also apply to the task of interactive communication (two-way communication) over a noisy channel. In a recent paper, Braverman and Rao [STOC 2011] show that any function of two inputs has a constant-rate interactive protocol for two users that withstands a noise rate up to 1/4. By assuming that the parties share a secret random string, we extend this result and construct an interactive protocol that succeeds with overwhelming probability against noise rates up to 1/2. We also show that no constant-rate protocol exists for noise rates above 1/2 for functions that require two-way communication. This is contrasted with our first result in which computing the "function" requires only one-way communication and the noise rate can go up to 1.

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“…Followup works by Braverman and Rao [BR11] and by Braverman [Bra12] showed how to improve the error rate to 1/8 (1/4 for non-binary alphabet) and how to improve the computational complexity to 2 Θ(N ) , respectively. Gelles, Moitra and Sahai [GMS11] showed that the computational complexity can be improved to poly(N ) if the channel errors are uniformly distributed (i.e. each bit is flipped with the same fixed probability), however their simulator still required exponential time for adversarial channels.…”

Section: Introductionmentioning

confidence: 99%

Fast Interactive Coding against Adversarial Noise

Brakerski

Kalai

Naor

2014

J. ACM

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Consider two parties who wish to communicate in order to execute some interactive protocol π. However, the communication channel between them is noisy: An adversary sees everything that is transmitted over the channel and can change a constant fraction of the bits arbitrarily, thus interrupting the execution of π (which was designed for an error-free channel). If π only contains a single long message, then a good error correcting code would overcome the noise with only a constant overhead in communication. However, this solution is not applicable to interactive protocols consisting of many short messages.Schulman (FOCS 92, STOC 93) introduced the notion of interactive coding: A simulator that, given any protocol π, is able to simulate it (i.e. produce its intended transcript) even in the presence of constant rate adversarial channel errors, and with only constant (multiplicative) communication overhead. However, the running time of Schulman's simulator, and of all simulators that followed, has been exponential (or sub-exponential) in the communication complexity of π (which we denote by N ).In this work, we present three efficient simulators, all of which are randomized and have a certain failure probability (over the choice of coins). The first runs in time poly(N ), has failure probability roughly 2 −N , and is resilient to 1 32 -fraction of adversarial error. The second runs in time O(N log N ), has failure probability roughly 2 −N , and is resilient to some constant fraction of adversarial error. The third runs in time O(N ), has failure probability 1/poly(N ), and is resilient to some constant fraction of adversarial error. (Computational complexity is measured in the RAM model.) The first two simulators can be made deterministic if they are a priori given a random string (which may be known to the adversary ahead of time). In particular, the simulators can be made to be non-uniform and deterministic (with equivalent performance). * This paper is the full version of "Efficient Interactive Coding Against Adversarial Noise" by Brakerski and Kalai (preliminary version FOCS 2012) and "Fast Algorithms for Interactive Coding" by Brakerski and Naor (preliminary version SODA 2013).

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Efficient and Explicit Coding for Interactive Communication

Cited by 61 publications

References 16 publications

Formulas Resilient to Short-Circuit Errors

Formulas Resilient to Short-Circuit Errors

Optimal Coding for Streaming Authentication and Interactive Communication

Fast Interactive Coding against Adversarial Noise

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