# 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} }

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…

## 86 Citations

### Capacity of Interactive Communication over Erasure Channels and Channels with Feedback

- Computer ScienceSIAM J. Comput.
- 2015

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.

### Towards Optimal Deterministic Coding for Interactive Communication

- Computer ScienceSODA
- 2015

The fact that the tree code is systematic, turns out to play an important role in obtaining rate 1 - O([EQUATION]) in the random error model, and approaching rate 1 in the adversarial error model.

### Interactive coding resilient to an unknown number of erasures

- Computer ScienceOPODIS
- 2019

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

- Computer ScienceIEEE Transactions on Information Theory
- 2016

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.

### Efficient Interactive Coding Achieving Optimal Error Resilience Over the Binary Channel

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2022

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

- Computer ScienceSODA
- 2016

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

- Computer Science, MathematicsPODC
- 2019

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

- Computer Science2014 IEEE 55th Annual Symposium on Foundations of Computer Science
- 2014

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

- Computer Science2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

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

- Computer ScienceJ. ACM
- 2015

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).

## References

SHOWING 1-10 OF 16 REFERENCES

### Capacity of Interactive Communication over Erasure Channels and Channels with Feedback

- Computer ScienceSIAM J. Comput.
- 2015

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

- Computer Science2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
- 2012

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

- Computer ScienceSODA
- 2013

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

- Computer ScienceIEEE Transactions on Information Theory
- 2015

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.

### Optimal error rates for interactive coding I: adaptivity and other settings

- Computer ScienceSTOC
- 2014

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

- Computer ScienceIEEE Transactions on Information Theory
- 2016

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

- Computer Science2014 IEEE 55th Annual Symposium on Foundations of Computer Science
- 2014

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

- Computer ScienceIEEE Transactions on Information Theory
- 2014

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

- Computer ScienceSTOC '13
- 2013

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

- Computer ScienceProceedings., 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.