A Lower Bound on the Interactive Capacity of Binary Memoryless Symmetric Channels
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The interactive capacity of a channel is defined in this paper as the maximal rate at which the transcript of any interactive protocol can be reliably simulated over the channel. It is shown that the interactive capacity of any binary memoryless symmetric (BMS) channel is at least 0.0302 its Shannon capacity. To that end, a rewind-if-error coding scheme for the simpler binary symmetric channel (BSC) is presented, achieving the lower bound for any crossover probability. The scheme is based on extended-Hamming codes combined with randomized error detection. The bound is then shown to hold for any BMS channel using extremes of the Bhattacharyya parameter. Finally, it is shown that the public randomness required for error detection can be reduced to private randomness in a standard fashion, and can be extracted from the channel without affecting the overall asymptotic rate. This gives rise to a fully deterministic interactive coding scheme achieving our lower bound over any BMS channel.
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