JAMMING-RESISTANT BACKOFF WITH POLYLOGARITHMIC SENDING AND LISTENING COST

Contention resolution addresses the problem of coordinating access to a shared communication channel. Time is discretized into synchronized slots, and a packet transmission can be made in any slot. A packet succeeds if it is the only packet transmitted during that slot. If two or more packets are sent in the same slot, then these packets collide and fail. Listening on the channel during a slot provides ternary feedback, indicating whether that slot had (0) silence, (1) a successful transmission, or (2+) noise. No other feedback or exchange of information is available to packets. Packets are (adversarially) injected into the system over time. A packet departs the system once it succeeds. The goal is to ensure all packets succeed, while optimizing throughput, which entails optimizing the fraction of successful slots. Most prior contention resolution algorithms with constant throughput require a short feedback loop, in the sense that a packet's sending probability in slot t+ 1 is fully determined by its internal state at slot t and the channel feedback at slot t. This paper answers the question of whether these short feedback loops are necessary; that is, how often must listening and updating occur in order to achieve constant throughput? A shared channel can also suffer random or adversarial noise (modeled as jamming), even when no packets are actually sent. How does noise affect our goal of long feedback loops/energy efficiency? Tying these questions together, we ask the following: What does a contention-resolution algorithm have to sacrifice to reduce channel accesses? Must we give up on constant throughput? What about robustness to noise? Here, we show that we need not concede anything by presenting an algorithm with the following guarantees. Suppose there are N packets arriving over time and J jammed slots, where the input is determined by an adaptive adversary. With high probability in N + J, our algorithm guarantees Θ(1) throughput and polylog(N + J ) channel accesses (sends or listens) per packet. We also have analogous guarantees when the input stream is infinite-we prove implicit throughput bounds of Ω(1) for all time slots t, and this translates to Θ(1) guaranteed throughput for any slot t where the implicit throughput is sufficiently small in Θ(1). As a special case, these throughput results give rise to adversarial-queuing theory guarantees.