Implementing the Abstract MAC Layer via Inductive Coloring Under the Rayleigh-Fading Model

Abstract

In this paper, we study distributed algorithms to realize efficient communications under the Rayleigh-fading model. This model extends the popular deterministic SINR model using stochastic propagations to address the fading effects observed in reality. Stochastic propagations can greatly increase the difficulty of handling interference and collisions, especially in a local context without much global knowledge. We present a new technique called Inductive Coloring that can be used to schedule fast transmissions with Rayleigh-fading interference. The computation of inductive coloring takes only O(log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> n) time with the proposed distributed algorithm, where n is the number of nodes in the network. We illustrate the power of inductive coloring by giving a distributed and randomized algorithm to implement the abstract MAC (absMAC) layer, which was first proposed by Kuhn et al.. With two basic time-guaranteed communication primitives, namely acknowledgement and progress, which correspond to the operations of node local broadcasts and message receptions from others, the absMAC layer decomposes the algorithm design and analysis in networks into two independent components, i.e., implementing the absMAC layer over a physical network and designing algorithms with the help of the two primitives in the absMAC layer. Thus, it sharply reduces the fussy and complicated process of algorithm design and analysis over the physical network. Our proposed algorithm implements the absMAC layer under the Rayleigh-fading model with no more than a logarithmic factor inferior to the optimal solution in terms of time complexity. The presented simulation results indicate that our algorithm performs well in realistic environments. Furthermore, we show that by making full use of our proposed absMAC layer algorithm, many network primitives such as Neighbor Discovery, Single/Multiple-Message Broadcast, and Consensus, can be efficiently implemented.