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Towards Coding for Maximum Errors in Interactive Communication Mark Braverman

Summary: Towards Coding for Maximum Errors in Interactive Communication
Mark Braverman
Anup Rao
We show that it is possible to encode any communication protocol between two parties so that the protocol
succeeds even if a (1/4 - ) fraction of all symbols transmitted by the parties are corrupted adversarially,
at a cost of increasing the communication in the protocol by a constant factor (the constant depends on
epsilon). This encoding uses a constant sized alphabet. This improves on an earlier result of Schulman, who
showed how to recover when the fraction of errors is bounded by 1/240. We also show how to simulate an
arbitrary protocol with a protocol using the binary alphabet, a constant factor increase in communication
and tolerating a 1/8 - fraction of errors.
1 Introduction
Suppose a sender wants to send an n bit message to a receiver, but some of the sender's transmissions may be
received incorrectly. What is the best way to encode the message in order to recover from the errors? This
question, first considered by Shannon [Sha48], initiated the study of error correcting codes, which have since
found applications in many different contexts. The book [PWJ72] is a good reference. In our work, we study the
analogous question in the more general setting of interactive communication. We refer the reader to the book
[KN97] for an introduction to interactive communication protocols. Most models of computation, for example
circuits, branching programs, streaming algorithms, distributed systems, inherently involve communication
protocols, so the following question is well motivated -- What is the best way to encode an arbitrary two party


Source: Anderson, Richard - Department of Computer Science and Engineering, University of Washington at Seattle


Collections: Computer Technologies and Information Sciences