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In high speed train (HST) system, real-time multimedia entertainments are very important applications in which a data stream often contains packets with different quality of service requirements. For example, video stream encoded with scalability contains the base layer packets with high quality (HQ) bit error rate (BER) requirement and enhancement layers' packets with low quality (LQ) BER requirement. When a conventional allocation approach, which only considers one BER constraint for one data stream, is applied to orthogonal frequency division multiple access (OFDMA) systems, the BER constraint will be the strictest one among multiple requirements from different types of packets, which leads to inefficient allocation when each data stream has multiple BER requirements. This paper aims to develop novel resource allocation approach by considering multiple BER requirements for different types of packets in one data stream. In order to not only simplify the resource allocation, but also to compensate for the channel estimation error caused by Doppler shift in the HST environment, a proper number of contiguous subcarriers are grouped into chunks and spectrum is allocated chunk by chunk. Simulation results show that the developed resource allocation scheme outperforms the conventional scheme, particularly when the BER ratio of HQ packets to LQ packets is larger than one. Furthermore, in order to reduce the complexity of resource allocation further, an empirical allocation scheme is proposed to allocate better chunks to HQ packets. It is shown that the performance of the empirical allocation scheme is quite close to that of the optimal scheme.