Interactive error resilience beyond 2/7

Interactive error correcting codes can protect interactive communication protocols against a constant fraction of adversarial errors, while incurring only a constant multiplicative overhead in the total communication. What is the maximum fraction of errors that such codes can protect against? For the non-adaptive channel, where the parties must agree in advance on the order in which they communicate, Braverman and Rao prove that the maximum error resilience is 1/4 (STOC, 2011). Ghaffari, Haeupler, and Sudan (STOC, 2014) consider the adaptive channel, where the order in which the parties communicate may not be fixed, and give a clever protocol that is resilient to a 2/7 fraction of errors. This was believed to be optimal. We revisit this result, and show how to overcome the 2/7 barrier. Specifically, we show that, over the adaptive channel, every two-party communication protocol can be converted to a protocol that is resilient to 7/24 > 2/7 fraction of errors with only a constant multiplicative overhead to the total communication. The protocol is obtained by a novel implementation of a feedback mechanism over the adaptive channel.

[1]  Avi Wigderson,et al.  Explicit Capacity Approaching Coding for Interactive Communication , 2018, IEEE Transactions on Information Theory.

[2]  Bernhard Haeupler,et al.  Synchronization Strings: Channel Simulations and Interactive Coding for Insertions and Deletions , 2017, ICALP.

[3]  Klim Efremenko,et al.  Interactive coding over the noisy broadcast channel , 2018, Electron. Colloquium Comput. Complex..

[4]  Ran Gelles,et al.  Coding for Interactive Communication: A Survey , 2017, Found. Trends Theor. Comput. Sci..

[5]  Alexander A. Sherstov,et al.  Optimal Interactive Coding for Insertions, Deletions, and Substitutions , 2017, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS).

[6]  Gang Wang,et al.  Communication with partial noisy feedback , 2017, 2017 IEEE Symposium on Computers and Communications (ISCC).

[7]  Mark Braverman,et al.  Coding for Interactive Communication Correcting Insertions and Deletions , 2017, IEEE Transactions on Information Theory.

[8]  Ameya Velingker,et al.  Bridging the Capacity Gap Between Interactive and One-Way Communication , 2017, SODA.

[9]  Klim Efremenko,et al.  Maximal Noise in Interactive Communication Over Erasure Channels and Channels With Feedback , 2015, IEEE Transactions on Information Theory.

[10]  Amit Sahai,et al.  Adaptive protocols for interactive communication , 2013, 2016 IEEE International Symposium on Information Theory (ISIT).

[11]  Ran Gelles,et al.  Capacity of Interactive Communication over Erasure Channels and Channels with Feedback , 2015, SIAM J. Comput..

[12]  Rafail Ostrovsky,et al.  Optimal Coding for Streaming Authentication and Interactive Communication , 2015, IEEE Transactions on Information Theory.

[13]  Ameya Velingker,et al.  Communication with Partial Noiseless Feedback , 2015, APPROX-RANDOM.

[14]  Yael Tauman Kalai,et al.  Fast Interactive Coding against Adversarial Noise , 2014, JACM.

[15]  Mark Braverman,et al.  List and Unique Coding for Interactive Communication in the Presence of Adversarial Noise , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[16]  Bernhard Haeupler,et al.  Interactive Channel Capacity Revisited , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[17]  Amit Sahai,et al.  Efficient Coding for Interactive Communication , 2014, IEEE Transactions on Information Theory.

[18]  Madhu Sudan,et al.  Optimal error rates for interactive coding I: adaptivity and other settings , 2013, STOC.

[19]  Bernhard Haeupler,et al.  Optimal Error Rates for Interactive Coding II: Efficiency and List Decoding , 2013, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[20]  Mark Braverman,et al.  Toward Coding for Maximum Errors in Interactive Communication , 2011, IEEE Transactions on Information Theory.

[21]  Ran Raz,et al.  Interactive channel capacity , 2013, STOC '13.

[22]  Denis Pankratov,et al.  On the Power of Feedback in Interactive Channels , 2013 .

[23]  Mark Braverman,et al.  Towards deterministic tree code constructions , 2012, ITCS '12.

[24]  Amit Sahai,et al.  Efficient and Explicit Coding for Interactive Communication , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[25]  Venkatesan Guruswami,et al.  Algorithmic Results in List Decoding , 2006, Found. Trends Theor. Comput. Sci..

[26]  Venkatesan Guruswami,et al.  Linear time encodable and list decodable codes , 2003, STOC '03.

[27]  L. Schulman.  Coding for interactive communication , 1995, Proceedings of 1995 IEEE International Symposium on Information Theory.

[28]  Leonard J. Schulman,et al.  Deterministic coding for interactive communication , 1993, STOC.

[29]  Leonard J. Schulman,et al.  Communication on noisy channels: a coding theorem for computation , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[30]  E. Berlekamp.  Block coding with noiseless feedback , 1964 .