Contention resolution addresses the problem of coordinating access to a shared channel. Time proceeds in slots, and a packet transmission can be made in any slot. A packet is successfully sent if no other packet is also transmitted during that slot. If two or more packets are sent in the same slot, then none of these transmissions succeed. Listening during a slot gives ternary feedback, indicating if that slot had (0) silence, (1) a successful transmission, or (2+) noise. No other feedback is available. Packets are (adversarially) injected into the system over time. A packet departs the system once it is successful. The goal is to send all packets while optimizing throughput, which is roughly the fraction of successful slots. Most prior 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. An open question is whether these short feedback loops are necessary; that is, how often must listening and updating occur in order to achieve constant throughput? This question addresses energy efficiency, since both listening and sending consume significant energy. The channel can also suffer adversarial noise ("jamming"), which causes any listener to hear noise, even when no packets are sent. How does jamming affect our goal of long feedback loops/energy efficiency? Connecting these questions, we ask: what does a contention-resolution algorithm have to sacrifice to reduce channel accesses? Must we give up on constant throughput or robustness to noise? Here, we show that we need not concede anything. Suppose there are N packets and J jammed slots, where the input is determined by an adaptive adversary. We give an algorithm that, with high probability in N+J, has constant throughput and polylog(N+J) channel accesses per packet.
翻译:竞争解决旨在协调对共享信道的访问。时间按时间槽推进,数据包可在任意时间槽内传输。若某时间槽内无其他数据包同时传输,则该数据包成功发送;若同一时间槽内有两个或更多数据包同时传输,则所有传输均告失败。监听时间槽可获取三种反馈结果,指示该时间槽为(0)静默、(1)成功传输或(2+)噪声。系统无法获得其他反馈。数据包随时间(对抗性地)注入系统,一旦成功发送即离开系统。目标是在优化吞吐量(大致为成功时间槽的比例)的同时完成所有数据包的发送。以往大多数具有恒定吞吐量的算法都需要短反馈环路,即数据包在时间槽t+1的发送概率完全由其时间槽t的内部状态和信道反馈决定。一个悬而未决的问题是:这些短反馈环路是否必要?换言之,为获得恒定吞吐量,监听和更新必须以何种频率进行?该问题涉及能效——因为监听和发送均消耗大量能量。信道还可能遭受对抗性噪声("干扰"),导致即使没有数据包发送,监听者也会听到噪声。干扰如何影响我们追求长反馈环路/能效的目标?综合这些问题,我们探究:为减少信道访问,竞争解决算法必须牺牲什么?是否必须放弃恒定吞吐量或抗噪性?本文证明无需做任何让步。假设存在N个数据包和J个受干扰的时间槽,输入由自适应对抗模型决定。我们提出的算法在N+J的高概率下具有恒定吞吐量,且每个数据包的信道访问次数为关于N+J的多对数级别。