Capacity Upper Bounds on Binary Deletion Channels

In this paper, we discuss the problem of bounding the capacity of binary deletion channels in light of the paper, “Tight Asymptotic Bounds for the Deletion Channel with Small Deletion Probabilities” (Kalai, Mitzenmacher, Sudan, 2010), which proves an upper bound of C ≤ 1 − (1 − o(1))H(p) for the capacity of a binary deletion channel for p approaching 0. We present a brief history surrounding the bounds on the Binary Deletion Channels (BDC). We then explain the proof presented in the paper, highlighting its key ideas, its connections to other results for deletion channels and its limitation to small deletion probabilities.