We investigate the efficacy of error correcting codes in improving the performance of underwater wireless optical communication systems. For this purpose, the effectiveness of several coding schemes, i.e., the classical Reed-Solomon and a recent family of low-density parity check codes, is studied in the physical (PHY) and the upper layers assuming negligible water turbulence. The presented numerical results testify to the interest of using efficient codes both at the PHY and upper protocol layers, although we are concerned by a non-fading channel. Furthermore, we discuss the choice of coding schemes and the appropriate degree of data protection in the PHY and upper layers.