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In this paper, we jointly optimize computation and communication task scheduling for streaming applications on MPSoC. The objective is to minimize schedule length by totally removing inter-core communication overhead. By minimizing schedule length, the system performance can be improved by adopting a smaller period or exploring the slacks generated for energy reduction with DVS. To guarantee the schedulability of communication tasks, we perform the schedulability analysis, and theoretically obtain the upper bound of the times needed to reschedule each computation task. Based on the analysis, we formulate the scheduling problem as an ILP (Integer Linear Programming) formulation and obtain an optimal solution. We evaluate our technique with a set of benchmarks from both real-life streaming applications and synthetic task graphs. The simulation results show that our technique can achieve a 27.72% reduction in schedule length and a 13.38% reduction in energy consumption on average compared with the previous work.