In high speed railways (HSRs) communication system, when a train travels along the railway with high velocity, the wireless channel between the train and base station varies strenuously, which makes it essential to implement appropriate power allocations to guarantee system performance. What's more, how to evaluate the performance limits in this new scenario is also needed to consider. To this end, this paper investigates the performance limits of wireless communication in HSRs scenario. Since the hybrid information transmitted between train and base station usually has diverse quality of service (QoS) requirements, QoS-based achievable rate region is utilized to characterize the transmission performance in this paper. It is proved that traditional ergodic capacity and outage capacity with unique QoS requirement can be regarded as two extreme cases of the achievable rate region proposed in this paper. The corresponding optimal power allocation strategy is also given to achieve the maximal boundary of achievable rate region. Compared with conventional strategies, the advantages of the proposed strategy are validated in terms of green communication, namely minimizing average transmit power. Besides, the hybrid information transmission in a non-uniform generalized motion scenario is analyzed to confirm the robust performance of proposed strategy. The performance loss caused by non-uniform motion compared with that in uniform motion is also indicated, where a deterministic worst case for instantaneous speed realization is proposed to serve as the lower bound for system performance.