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The forthcoming Versatile Video Coding (VVC) standard adopts the trellis-coded quantization, which leverages the delicate trellis graph to map the quantization candidates within one block into the optimal path. Despite the high compression efficiency, the complex trellis search with soft decision quantization may hinder the applications due to high complexity and low throughput capacity. To reduce the complexity, in this paper, we propose a low complexity trellis-coded quantization scheme in a scientifically sound way with theoretical modeling of the rate and distortion. As such, the trellis departure point can be adaptively adjusted, and unnecessarily visited branches are accordingly pruned, leading to the shrink of total trellis stages and simplification of transition branches. Extensive experimental results on the VVC test model show that the proposed scheme is effective in reducing the encoding complexity by 11% and 5% with all intra and random access configurations, respectively, at the cost of only 0.11% and 0.05% BD-Rate increase. Meanwhile, on average 24% and 27% quantization time savings can be achieved under all intra and random access configurations. Due to the excellent performance, the VVC test model has adopted one implementation of the proposed scheme.