Binary Interactive Error Resilience Beyond

Efremenko, Klim; Kol, Gillat; Saxena, Raghuvansh R.

doi:10.1109/focs46700.2020.00051

Cited by 7 publications

(5 citation statements)

References 22 publications

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“…[BR11] presented the first error-resilient protocol over the binary channel, achieving an error resilience of 1 8 . This was later improved to 5 in [EKS20], and finally to 1 6 in the work of [GZ21]. 1 6 is known to be optimal.…”

Section: Interactive Codingmentioning

confidence: 99%

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Interactive Error Correcting Codes Over Binary Erasure Channels Resilient to $>\frac12$ Adversarial Corruption

Gupta¹,

Kalai²,

Zhang³

2021

Preprint

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An error correcting code (ECC) allows a sender to send a message to a receiver such that even if a constant fraction of the communicated bits are corrupted, the receiver can still learn the message correctly. Due to their importance and fundamental nature, ECCs have been extensively studied, one of the main goals being to maximize the fraction of errors that the ECC is resilient to.For adversarial erasure errors (over a binary channel) the maximal error resilience of an ECC is 1 2 of the communicated bits. In this work, we break this 1 2 barrier by introducing the notion of an interactive error correcting code (iECC) and constructing an iECC that is resilient to adversarial erasure of 3 5 of the total communicated bits. We emphasize that the adversary can corrupt both the sending party and the receiving party, and that both parties' rounds contribute to the adversary's budget.We also prove an impossibility (upper) bound of 2 3 on the maximal resilience of any binary iECC to adversarial erasures. In the bit flip setting, we prove an impossibility bound of 2 7 .

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Section: Interactive Codingmentioning

confidence: 99%

“…We begin by discussing a simpler scheme that achieves an error resilience over the binary erasure channel of 6 11 − . 5 Our starting point is based on the list-decoding to unique-decoding paradigm of [GH13,EKS20].…”

Section: A Simpler 6/11 Ieccmentioning

confidence: 99%

Interactive Error Correcting Codes Over Binary Erasure Channels Resilient to $>\frac12$ Adversarial Corruption

Gupta¹,

Kalai²,

Zhang³

2021

Preprint

View full text Add to dashboard Cite

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“…There are two works improving the error resilience beyond 1 8 . The first is [EKS20]. Their protocol is resilient to 5 39 error, and is positive rate but inefficient.…”

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%

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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“…There has been some recent work towards this goal. Over the binary bit flip channel, [EKS20] broke the 1 8 barrier for the first time, describing a protocol that achieves 5 39 resilience to adversarial bit flips. Over the binary erasure channel, [EGH16] gives a protocol achieving a 1 3 resilience to erasures.…”

Section: Introductionmentioning

confidence: 99%

The Optimal Error Resilience of Interactive Communication Over Binary Channels

Gupta¹,

Zhang²

2021

Preprint

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In interactive coding, Alice and Bob wish to compute some function f of their individual private inputs x and y. They do this by engaging in a non-adaptive (fixed order, fixed length) protocol to jointly compute f (x, y). The goal is to do this in an error-resilient way, such that even given some fraction of adversarial corruptions, both parties still learn f (x, y).In this work, we study the optimal error resilience of such a protocol in the face of adversarial bit flip or erasures. While the optimal error resilience of such a protocol over a large alphabet is well understood, the situation over the binary alphabet has remained open. In this work, we resolve this problem of determining the optimal error resilience over binary channels. In particular, we construct protocols achieving 1 6 error resilience over the binary bit flip channel and 1 2 error resilience over the binary erasure channel, for both of which matching upper bounds are known. We remark that the communication complexity of our binary bit flip protocol is polynomial in the size of the inputs, and the communication complexity of our binary erasure protocol is linear in the size of the minimal noiseless protocol computing f .

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Binary Interactive Error Resilience Beyond

Cited by 7 publications

References 22 publications

Interactive Error Correcting Codes Over Binary Erasure Channels Resilient to $>\frac12$ Adversarial Corruption

Interactive Error Correcting Codes Over Binary Erasure Channels Resilient to $>\frac12$ Adversarial Corruption

Efficient Interactive Coding Achieving Optimal Error Resilience Over the Binary Channel

The Optimal Error Resilience of Interactive Communication Over Binary Channels

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