The performance of the coded generalized frequency division multiplexing (GFDM) transceiver has been evaluated in a shallow underwater acoustic channel (UAC). Acoustic transmission is the scheme of choice for communication in UAC since radio waves suffer from absorption and light waves scatter. Although orthogonal frequency division multiplexing (OFDM) has found its ground for multicarrier acoustic underwater communication, it suffers from high peak to average power ratio (PAPR) and out of band (OOB) emissions. We propose a coded-GFDM based multicarrier system since GFDM has a higher spectral efficiency compared to a traditional OFDM system. In doing so, we assess two block codes, namely Bose, Chaudari, and Hocquenghem (BCH) codes, Reed-Solomon (RS) codes, and several convolutional codes. We present the error performances of these codes when used with GFDM. Furthermore, we evaluate the performance of the proposed system using two equalizers: Matched Filter (MF) and Zero-Forcing (ZF). Simulation results show that among the various block coding schemes that we tested, BCH (31,6) and RS (15,3) give the best error performance. Among the convolutional codes that we tested, rate 1/4 convolutional codes give the best performance. However, the performance of BCH and RS codes is much better than the convolutional codes. Moreover, the performance of the ZF equalizer is marginally better than the MF equalizer. In conclusion, using the channel coding schemes with GFDM improves error performance manifolds thereby increasing the reliability of the GFDM system despite slightly higher complexity.