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The trellis source coding theorem for any discrete-time stationary Gaussian source with the squared-error distortion measure is proved by Mazor and Pearlman. From their results, we constructed a trellis with the constraint length, K, equal to 3,the branching factor, q, qual to 8, and the block size, N, equal to 128. In this paper, we present a training algorithm for this transform trellis codebook which uses the M-lgorithm to search the trellis codebook and LBG algorithm to update the trellis codebook. For the first -order autoregressive Gaussian source whose correlation coefficient is 0. 9, we investigated the trained transform trellis coding scheme from rate 0. 07 to 1. 0 bits/sample. The achieved SNR for the test sequence is from 0. 6 to 1. 4 dB less than the theoretical SNR, depending on the rate, and surpasses all previous known results for this source
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