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We provide a new fuzzy relaxation trellis codebook search algorithm over noisy channels. The new algorithm solves the problems associated with the LBG algorithm in the sense of delivering relatively lower distortion configurations using short training sequences. Furthermore, the new approach is significantly less sensitive to the initialization process. The algorithm minimizes a weighted distortion measure averaged over both the source and the channel statistics. The weights are soft distortion-related reliability information, which are delivered by a soft trellis vector quantization algorithm (STVQ). The concept of soft compression is introduced by Haddad and Yongacoglu (see Proc. GLOBECOM, Rio de Janeiro, Brazil, Dec. 1999) in another paper, using the forward-backward symbol-MAP algorithm. The work introduced in this paper is an extension of the work established for the noiseless channel case by Haddad and Yongacoglu (see Proc. IEEE ICASSP, Istanbul, Turkey, June 2000) in yet another paper. Testing is performed using first- and second-order Gauss-Markov sources over several trellis structures, vector dimensions, and compression rates. Moreover, the robustness of the optimal configurations is tested under channel-mismatch conditions and compared with tandem coding systems.