In this paper, improved code-shift keying (CSK) systems with a functional pseudonoise (PN) code are considered for use in indoor optical-wireless channels. In CSK, increasing the number of optical PN codes improves the data rate. It is also effective for increasing the number of simultaneously transmitting optical PN codes. This method is named N-parallel CSK (N-CSK), which indicates the transmission of N codes. In order to enhance the data rate of CSK systems, optical PN code design has become one of the key areas of study. As such functional codes, in this paper we consider EPOM and POEPC, which can be generated by fusing two kinds of optical PN codes. CSK systems can implement two-stage demodulation, which demodulates every optical PN code. It is expected that two-stage demodulation will improve the bit error rate (BER) performance of CSK systems. In this paper, we combine two-stage demodulation with CSK systems: CSK using EPOM and N-CSK using POEPC. It was found that the BER of CSK systems can be improved by utilizing two-stage demodulation.