In this paper, we consider a dense vehicular communication network where each vehicle broadcasts its safety information to its neighborhood in each transmission period. Such applications require low latency and high reliability, and thus, we exploit non-orthogonal multiple access to reduce the access latency and to improve the packet reception probability. In the proposed two-fold scheme, the BS performs semi-persistent scheduling and allocates time-frequency resources in a nonorthogonal manner while the vehicles autonomously perform distributed power control with iterative signaling control. We formulate the centralized scheduling and resource allocation problem as equivalent to a multi-dimensional stable roommate matching problem, in which the users and time/frequency resources are considered as disjoint sets of objects to be matched with each other. We then develop a novel rotation matching algorithm, which converges to an L-rotation stable matching after a limited number of iterations. Simulation results show that the proposed scheme outperforms the traditional orthogonal multiple access scheme in terms of the access latency and reliability.