  In this paper, we consider contention resolution on a multiple-access
communication channel. In this problem, a set of nodes arrive over time, each
with a message it intends to send. In each time slot, each node may attempt to
broadcast its message or remain idle. If a single node broadcasts in a slot,
the message is received by all nodes; otherwise, if multiple nodes broadcast
simultaneously, a collision occurs and none succeeds. If collision detection is
available, nodes can differentiate collision and silence (i.e., no nodes
broadcast). Performance of contention resolution algorithms is often measured
by throughput -- the number of successful transmissions within a period of
time; whereas robustness is often measured by jamming resistance -- a jammed
slot always generates a collision. Previous work has shown, with collision
detection, optimal constant throughput can be attained, even if a constant
fraction of all slots are jammed. The situation when collision detection is not
available, however, remains unclear.
  In a recent breakthrough paper [Bender et al., STOC '20], a crucial case is
resolved: constant throughput is possible without collision detection, but only
if there is no jamming. Nonetheless, the exact trade-off between the best
possible throughput and the severity of jamming remains unknown. In this paper,
we address this open question. Specifically, for any level of jamming ranging
from none to constant fraction, we prove an upper bound on the best possible
throughput, along with an algorithm attaining that bound. An immediate and
interesting implication of our result is, when a constant fraction of all slots
are jammed, which is the worst-case scenario, there still exists an algorithm
achieving a decent throughput: $\Theta(t/\log{t})$ messages could be
successfully transmitted within $t$ slots.
