| Description |
We study the relation between public and private-coin information complexity. Improving a recent result by Brody et al., we prove that a one-round private-coin protocol with information cost I can be simulated by a one-round public-coin protocol with information cost \le I + \log(I) + O(1). This question is connected to the question of compression of interactive protocols and direct sum for communication complexity.
We also give a lower bound. We exhibit a one-round private-coin protocol with information cost ~ n/2 - \log(n) which cannot be simulated by any public-coin protocol with information cost n/2 - O(1). This example also explains an additive \log factor incurred in the study of communication complexity of correlations by Harsha et al.
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