Communication with Partial Noiseless Feedback

We introduce the notion of one-way communication schemes with partial noiseless feedback. In this setting, Alice wishes to communicate a message to Bob by using a communication scheme that involves sending a sequence of bits over a channel while receiving feedback bits from Bob for δ fraction of the transmissions. An adversary is allowed to corrupt up to a constant fraction of Alice’s transmissions, while the feedback is always uncorrupted. Motivated by questions related to coding for interactive communication, we seek to determine the maximum error rate, as a function of 0 ≤ δ ≤ 1, such that Alice can send a message to Bob via some protocol with δ fraction of noiseless feedback. The case δ = 1 corresponds to full feedback, in which the result of [1] implies that the maximum tolerable error rate is 1/3, while the case δ = 0 corresponds to no feedback, in which the maximum tolerable error rate is 1/4, achievable by use of a binary error-correcting code. In this work, we show...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Bernhard Haeupler, Pritish Kamath, Ameya Velingker
• Keywords: Algorithms, APPROX 2015