Avalanche photodiodes (APD) are widely employed in visible light communication (VLC) systems. The general signal dependent Gaussian channel is investigated. Experiment results reveal that symbols on different constellation points under official illuminance inevitably suffer from different levels of noise due to the multiplication process of APDs. In such a case, conventional log likely-hood ratio (LLR) calculation for signal independent channels may cause performance loss. The optimal LLR calculation for decoder is then derived because of the existence of non-ignorable APD shot noise. To find the decoding thresholds of the optimal and suboptimal detection schemes, the extrinsic information transfer (EXIT) chat is further analyzed. Finally a modified minimum sum algorithm is suggested with reduced complexity and acceptable performance loss. Numerical simulations show that, with a regular (3, 6) low-density parity check (LDPC) code of block length 20,000, 0.7 dB gain is achieved with our proposed scheme over the LDPC decoder designed for signal independent noise. It is also found that the coding performance is improved for a larger modulation depth.