An iterative, low-complexity soft-detection (SD) receiver is designed for detecting permutation-aided space-time shift keying (STSK) modulation in an indoor visible light communication (VLC) channel. The indices of the transmitters, which are light emitting diodes (LEDs) are coordinated by antenna matrices using permutations. Therefore, each index is selected only once at each transmit time and transmit block. However, the maximum likelihood (ML) detection becomes complex as the size of the LEDs increase and the STSK scheme requires knowledge of the channel state information (CSI). The proposed SD receiver uses the soft information from the channel to detect the likely transmitted symbols by interpreting the channel output as an assignment problem. The proposed receiver is capable of estimating the likely transmitted symbols with or without the knowledge of the CSI. Results are shown comparing the bit error rate (BER) of the ML receiver with perfect knowledge of the CSI with the SD receiver. The SD receiver matches the ML in cases where higher data rates are required and CSI is known but shows a 5dB loss without the knowledge of the CSI.