Optimal coding for streaming authentication and interactive communication

Matthew Franklin, Ran Gelles, Rafail Ostrovsky, Leonard J. Schulman

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

We consider the task of communicating a data stream-a long, possibly infinite message not known in advance to the sender-over a channel with adversarial noise. For any given noise rate c < 1 , we show an efficient, constant-rate scheme that correctly decodes a (1-c) fraction of the stream sent so far with high probability, or aborts if the noise rate exceeds c. In addition, we prove that no constant-rate scheme can recover more than a (1-c) fraction of the stream sent so far with non-negligible probability, which makes our scheme optimal in that aspect. The parties are assumed to preshare a random string unknown to the channel. Our techniques can also be applied to the task of interactive communication (two-way communication) over a noisy channel. In a recent paper (Braverman and Rao, STOC11), the possibility of two-party interactive communication as long as the noise level is < 1/4 was shown. By allowing the parties to preshare some private random string, we extend this result and construct a (nonefficient) constant-rate interactive protocol that succeeds with overwhelming probability against noise rates up to 1/2. We complete this result by proving that no constant-rate protocol can withstand noise rates > 1/2.

Original languageEnglish
Article number6951428
Pages (from-to)133-145
Number of pages13
JournalIEEE Transactions on Information Theory
Volume61
Issue number1
DOIs
StatePublished - 1 Jan 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

  • Blueberry codes
  • Data streams
  • adversarial noise
  • interactive communication
  • reliable communication
  • tree codes

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