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A Lower Bound on the Interactive Capacity of Binary Memoryless Symmetric Channels
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