Exact Implementation of Abstract MAC Layer via Carrier Sensing

In this paper, we present the first algorithm for exactly implementing the abstract MAC (absMAC) layer in the physical SINR model. The absMac layer, first presented by Kuhn et al. in [15], provides reliable local broadcast communication, with timing guarantees stated in terms of a collection of abstract delay functions, such that high-level algorithms can be designed in terms of these functions, independent of specific channel behavior. The implementation of absMAC layer is to design a distributed algorithm for the local broadcast communication primitives over a particular communication model that defines concrete channel behaviors, and the objective is minimizing the bounds of the abstract delay functions. Halldórsson et al. [10] have shown that in the standard SINR model (synchronous communication, without physical carrier sensing or location information), there cannot be efficient exact implementations. In this work, we show that physical carrier sensing, a commonly seen function performed by wireless devices, can help get efficient exact implementation algorithms. Specifically, we propose an algorithm that exactly implements the absMAC layer. The algorithm provides asymptotically optimal bounds for both acknowledgement and progress functions defined in the absMAC layer. Our algorithm can lead to many new faster algorithms for solving high-level problems in the SINR model. We demonstrate this by giving algorithms for problems of Consensus, Multi-Message Broadcast and Single-Message Broadcast. It deserves to point out that our implementation algorithm is designed based on an optimal algorithm for a General Local Broadcast (GLB) problem, which takes the number of distinct messages into consideration for the first time. The GLB algorithm can handle much more communication scenarios apart from those defined in the absMAC layer. Simulation results show that our proposed algorithms perform well in reality.