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This paper considers the problem of digital data transmission through the Global System for Mobile communications (GSM) for security applications. A data modem is presented that utilizes codebooks of Speech-Like (SL) symbols to transmit data through the GSM Adaptive Multi Rate (AMR) voice codec. Using this codebook of finite alphabet, the continuous vocoder channel is modeled by a Discrete Memory less Channel (DMC). A heuristic optimization algorithm is proposed to select codebook symbols from a database of observed human speech such that the capacity of DMC is maximized. Using the DMC capacity, a lower bound on the capacity of the considered voice channel can be achieved. Simulation results show that the proposed data modem achieves higher data rates and lower symbol error rates compared to previously reported results while requiring lower computational complexity for codebook optimization.