The optimal error resilience of interactive communication over binary channels

Gupta, Mridula; Zhang, Rachel Yun

doi:10.1145/3519935.3519985

Cited by 2 publications

(10 citation statements)

References 21 publications

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“…The protocol of [EGH16] relies on feedback for a "guess" of the transcript so far, and then the party responds according to whether or not they agree with this guess. The protocol of [GZ22] (achieving 1 6 error resilience in channels without feedback, but inefficiently) also uses this idea, however providing (unreliable) feedback through future messages instead. One step in our protocol uses this idea as well, following the blueprint of the construction in [GZ22].…”

Section: Interactive Codingmentioning

confidence: 99%

“…The protocol of [GZ22] (achieving 1 6 error resilience in channels without feedback, but inefficiently) also uses this idea, however providing (unreliable) feedback through future messages instead. One step in our protocol uses this idea as well, following the blueprint of the construction in [GZ22].…”

Section: Interactive Codingmentioning

confidence: 99%

“…Their protocol is resilient to 5 39 error, and is positive rate but inefficient. The second is [GZ22], which constructs a scheme achieving the optimal 1 6 -error resilience. However, both the communication and computational complexity can be up to exponential in the length of π 0 .…”

Section: Introductionmentioning

confidence: 99%

“…Efficient? Error Resilience [GH13] yes yes 1/8 [EKS20] yes no 5/39 [GZ22] no no 1/6 (optimal) This work yes yes 1/6 (optimal)…”

Section: Introductionmentioning

confidence: 99%

“…Ideally, the resulting scheme π should be positive rate, computationally efficient, and achieve optimal error resilience.While interactive coding over large alphabets is well understood, the situation over the binary alphabet has remained evasive. At the present moment, the known schemes over the binary alphabet that achieve a higher error resilience than a trivial adaptation of large alphabet schemes are either still suboptimally error resilient [EKS20], or optimally error resilient with exponential communication complexity [GZ22]. In this work, we construct a scheme achieving optimality in all three parameters: our protocol is positive rate, computationally efficient, and resilient to the optimal 1 6 − ǫ adversarial errors.…”

mentioning

confidence: 99%

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Efficient Interactive Coding Achieving Optimal Error Resilience Over the Binary Channel

Gupta¹,

Zhang²

2022

Preprint

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Given a noiseless protocol π 0 computing a function f (x, y) of Alice and Bob's private inputs x, y, the goal of interactive coding is to construct an error-resilient protocol π computing f such that even if some fraction of the communication is adversarially corrupted, both parties still learn f (x, y). Ideally, the resulting scheme π should be positive rate, computationally efficient, and achieve optimal error resilience.While interactive coding over large alphabets is well understood, the situation over the binary alphabet has remained evasive. At the present moment, the known schemes over the binary alphabet that achieve a higher error resilience than a trivial adaptation of large alphabet schemes are either still suboptimally error resilient [EKS20], or optimally error resilient with exponential communication complexity [GZ22]. In this work, we construct a scheme achieving optimality in all three parameters: our protocol is positive rate, computationally efficient, and resilient to the optimal 1 6 − ǫ adversarial errors. Our protocol employs a new type of code that we call a layered code, which may be of independent interest. Like a tree code, a layered code allows the coder to encode a message in an online fashion, but is defined on a graph instead of a tree.

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Section: Interactive Codingmentioning

confidence: 99%

Section: Interactive Codingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Efficient? Error Resilience [GH13] yes yes 1/8 [EKS20] yes no 5/39 [GZ22] no no 1/6 (optimal) This work yes yes 1/6 (optimal)…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%