Interactive Channel Capacity Revisited

@article{Haeupler2014InteractiveCC,
  title={Interactive Channel Capacity Revisited},
  author={Bernhard Haeupler},
  journal={2014 IEEE 55th Annual Symposium on Foundations of Computer Science},
  year={2014},
  pages={226-235}
}
  • Bernhard Haeupler
  • Published 6 August 2014
  • Computer Science
  • 2014 IEEE 55th Annual Symposium on Foundations of Computer Science
We provide the first capacity approaching coding schemes that robustly simulate any interactive protocol over an adversarial channel that corrupts any fraction of the transmitted symbols. Our coding schemes achieve a communication rate of 1 - O(∈√loglog1/∈) can be improved to 1 - O(√∈) for random, oblivious, and over any adversarial channel. This computationally bounded channels, or if parties have shared randomness unknown to the channel. Surprisingly, these rates exceed the 1 - Ω( H(ϵ)) = 1… 

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Interactive coding resilient to an unknown number of erasures

Interactive coding schemes are developed that adapt to the actual level of noise and correctly execute any two-party computation and succeed regardless of the amount of erasures.

Maximal Noise in Interactive Communication Over Erasure Channels and Channels With Feedback

This work provides tight upper and lower bounds on the noise resilience of interactive communication over noisy channels with feedback and provides a simple and efficient nonadaptive coding scheme that succeeds as long as the fraction of noise is at most 1/3 - ε.

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This work constructs a scheme achieving optimality in all three parameters: the protocol is positive rate, computationally efficient, and resilient to the optimal 16 − ϵ adversarial errors.

Bridging the Capacity Gap Between Interactive and One-Way Communication

This work shows that the capacity gap between one-way and interactive communication can be bridged even for very small (constant in $\epsilon$) average message lengths, which are likely to be found in many applications.

Efficient Multiparty Interactive Coding for Insertions, Deletions, and Substitutions

This work considers synchronous communication networks over an arbitrary topology, in the powerful adversarial insertion-deletion noise model, and provides efficient, constant rate schemes that successfully conduct any computation with high probability as long as the adversary corrupts at most ε over m fraction of the total communication.

List and Unique Coding for Interactive Communication in the Presence of Adversarial Noise

This paper precisely characterize the region of all pairs (α, β) for which one-sided unique decoding is possible in a way that Alice will output the correct answer and suggests that in some error regimes, list-decoding is necessary for optimal unique decoding.

Adaptive protocols for interactive communication

Adaptivity circumvents an impossibility result of 1/4 on the fraction of tolerable noise (Braverman and Rao, 2014) and demonstrates a protocol that tolerates noise rates up to 2/3.

Constant-Rate Coding for Multiparty Interactive Communication Is Impossible

Borders prove that, despite several previous coding schemes with rate Ω (1) for certain topologies, no coding scheme with constant rateΩ ( 1) exists for arbitrary n-party noisy networks, and the capacity of (synchronous) star networks is Θ (log log n/log n).
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References

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Capacity of Interactive Communication over Erasure Channels and Channels with Feedback

Coding schemes that simulate any alternating interactive protocol with rate 1 − Θ(H(e)) are shown, which implies a large asymptotic gap between interactive communication rate over noisy channels with and without feedback.

Efficient Interactive Coding against Adversarial Noise

This work shows how to efficiently simulate any interactive protocol in the presence of constant-rate adversarial noise, while incurring only a constant blow-up in the communication complexity (CC).

Fast Algorithms for Interactive Coding

The computational complexity of interactive coding is improved, while at least N computational steps are required (even just to output the transcript of π), the BK simulator runs in time.

Optimal Coding for Streaming Authentication and Interactive Communication

This work considers the task of communicating a data stream over a channel with adversarial noise, and constructs a (nonefficient) constant-rate interactive protocol that succeeds with overwhelming probability against noise rates up to 1/2, and proves that no constant- rate protocol can withstand noise rates > 1/1.

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A strong working hypothesis is set forward which stipulates that for any setting the maximum tolerable error rate is independent of many computational and communication complexity measures and believed to be a powerful guideline for the design of simple, natural, and efficient coding schemes.

Maximal Noise in Interactive Communication Over Erasure Channels and Channels With Feedback

This work provides tight upper and lower bounds on the noise resilience of interactive communication over noisy channels with feedback and provides a simple and efficient nonadaptive coding scheme that succeeds as long as the fraction of noise is at most 1/3 - ε.

List and Unique Coding for Interactive Communication in the Presence of Adversarial Noise

This paper precisely characterize the region of all pairs (α, β) for which one-sided unique decoding is possible in a way that Alice will output the correct answer and suggests that in some error regimes, list-decoding is necessary for optimal unique decoding.

Toward Coding for Maximum Errors in Interactive Communication

We show that it is possible to encode any communication protocol between two parties so that the protocol succeeds even if a (1/4 - ϵ) fraction of all symbols transmitted by the parties are corrupted

Interactive channel capacity

For a small enough ε, this result gives the first separation between interactive and non-interactive channel capacity, answering an open problem by Schulman [Schulman1].

Communication on noisy channels: a coding theorem for computation

  • L. Schulman
  • Computer Science
    Proceedings., 33rd Annual Symposium on Foundations of Computer Science
  • 1992
The author relates the noisy channel and the standard (noise less channel) complexities of a communication problem by establishing a 'two-way' or interactive analogue of Shanon's coding theorem, which involves simulating the original protocol while implementing a hierarchical system of progress checks which ensure that errors of any magnitude in the simulation are, with high probability, rapidly eliminated.