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We study communication models for channels with erasures in which the erasure pattern can be controlled by an adversary with partial knowledge of the transmitted codeword. In particular, we design block codes for channels with binary inputs with an adversary who can erase a fraction p of the transmitted bits. We consider causal adversaries, who must choose to erase an input bit using knowledge of that bit and previously transmitted bits, and myopic adversaries, who can choose an erasure pattern based on observing the transmitted codeword through a binary erasure channel with random erasures. For both settings we design efficient (polynomial time) encoding and decoding algorithms that use randomization at the encoder only. Our constructions achieve capacity for the causal and “sufficiently myopic” models. For the “insufficiently myopic” adversary, the capacity is unknown, but existing converses show the capacity is zero for a range of parameters. For all parameters outside of that range, our construction achieves positive rates. 

A source generates time-stamped update packets that are sent to a server and then forwarded to a monitor. This occurs in the presence of an adversary that can infer information about the source by observing the output process of the server. The server wishes to release updates in a timely way to the monitor but also wishes to minimize the information leaked to the adversary. We analyze the trade-off between the age of information (AoI) and the maximal leakage for systems in which the source generates updates as a Bernoulli process. For a time slotted system in which sending an update requires one slot, we consider three server policies: (1) Memoryless with Bernoulli Thinning (MBT): arriving updates are queued with some probability and head-of-line update is released after a geometric holding time; (2) Deterministic Accumulate-and-Dump (DAD): the most recently generated update (if any) is released after a fixed time; (3) Random Accumulate-and-Dump (RAD): the most recently generated update (if any) is released after a geometric waiting time. We show that for the same maximal leakage rate, the DAD policy achieves lower age compared to the other two policies but is restricted to discrete age-leakage operating points.