论文标题
大规模随机访问中无碰撞调度的最低反馈
Minimum Feedback for Collision-Free Scheduling in Massive Random Access
论文作者
论文摘要
考虑一个大规模的随机访问方案,其中需要在$ b \ ge k $插槽中安排大量$ n $潜在用户中的一小部分$ k $ active用户。确保调度无碰撞所需的用户所需的最低常见反馈是什么? Instead of a naive scheme of listing the indices of the $k$ active users in the order in which they should transmit, at a cost of $k\log(n)$ bits, this paper shows that for the case of $b=k$, the rate of the minimum fixed-length common feedback code scales only as $k \log(e)$ bits, plus an additive term that scales in $n$ as $Θ\left(\log \log(n) \ right)$ for固定$ k $。如果可以使用可变长度代码,假设用户之间的活动统一活动,则最低平均常见反馈率仍然需要$ k \ log(e)$位,但是对$ n $的依赖性可以降低到$ o(1)$。当$ b> k $时,可以大大减少无碰撞调度所需的反馈位数。此外,对于$ k \ le mb $,在每个插槽安排$ m $用户的情况下,也得出了对最低反馈率的类似规模。构建最小无碰撞反馈计划代码的问题与构建完美的哈希家族的问题相连,该家族允许使用完美的哈希算法构建实用的反馈计划代码。
Consider a massive random access scenario in which a small set of $k$ active users out of a large number of $n$ potential users need to be scheduled in $b\ge k$ slots. What is the minimum common feedback to the users needed to ensure that scheduling is collision-free? Instead of a naive scheme of listing the indices of the $k$ active users in the order in which they should transmit, at a cost of $k\log(n)$ bits, this paper shows that for the case of $b=k$, the rate of the minimum fixed-length common feedback code scales only as $k \log(e)$ bits, plus an additive term that scales in $n$ as $Θ\left(\log \log(n) \right)$ for fixed $k$. If a variable-length code can be used, assuming uniform activity among the users, the minimum average common feedback rate still requires $k \log(e)$ bits, but the dependence on $n$ can be reduced to $O(1)$. When $b>k$, the number of feedback bits needed for collision-free scheduling can be significantly further reduced. Moreover, a similar scaling on the minimum feedback rate is derived for the case of scheduling $m$ users per slot, when $k \le mb$. The problem of constructing a minimum collision-free feedback scheduling code is connected to that of constructing a perfect hashing family, which allows practical feedback scheduling codes to be constructed from perfect hashing algorithms.