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In this paper, we consider the capacity C of the binary deletion channel for the limiting case where the deletion probability p goes to 0. It is known that for any p <; 1/2, the capacity satisfies C ≥ 1-H(p), where H is the standard binary entropy. We show that this lower bound is essentially tight in the limit, by providing an upper bound C ≤ 1-(1-o(1))H(p), where the o(1) term is understood to...
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