Binary Error-Correcting Codes with Minimal Noiseless Feedback

In the setting of error-correcting codes with feedback, Alice wishes to communicate a k-bit message x to Bob by sending a sequence of bits over a channel while noiselessly receiving feedback from Bob. It has been long known (Berlekamp, 1964) that in this model, Bob can still correctly determine x even if ≈ 1/3 of Alice’s bits are flipped adversarially. This improves upon the classical setting without feedback, where recovery is not possible for error fractions exceeding 1/4.