Alice and Bob want to run a protocol over a noisy channel, where a certain number of bits are flipped adversarially. Several results take a protocol requiring @math bits of noise-free communication and make it robust over such a channel. In a recent breakthrough result, Haeupler described an algorithm that sends a number of bits that is conjectured to be near optimal in such a model. However, his algorithm critically requires @math knowledge of the number of bits that will be flipped by the adversary. We describe an algorithm requiring no such knowledge. If an adversary flips @math bits, our algorithm sends @math bits in expectation and succeeds with high probability in @math . It does so without any @math knowledge of @math . Assuming a conjectured lower bound by Haeupler, our result is optimal up to logarithmic factors. Our algorithm critically relies on the assumption of a private channel. We show that privacy is necessary when the amount of noise is unknown.
Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.