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This paper deals with the improvement of the Dirty Paper Trellis Code (DPTC) watermarking algorithm. This watermarking algorithm is known to be one of the best among the high rate watermarking schemes. Nevertheless, recent researches reveal its security weakness. Previously, we proposed to reinforce its security by using a secret space before the embedding. This secret space requires to compute projections onto secrets carriers. When dealing with high rate watermarking, the CPU cost for those projections is dramatically high. After introducing the watermarking scheme, we then propose two Space Division Multiplexing (SDM) approaches which reduce the complexity. Evaluations are achieved with four different attacks and show that our proposal gives better robustness results with SDM approaches.