We propose a novel channel model of satellite-to-ground optical transmission to achieve a global-scale high-capacity communication network. In addition, we compose an effective channel coding scheme based on low-density generator matrix (LDGM) code suitable for that channel. Because the first successful optical satellite communication demonstrations are quite recent, no practical channel model has been introduced. We analyze the results of optical transmission experiments between ground station and the Optical Inter-orbit Communications Engineering Test Satellite (OICETS) performed by NICT and JAXA in 2008 and propose a new Markov-based practical channel model. Furthermore, using this model we design an effective long erasure code (LEC) based on LDGM to achieve high-quality wireless optical transmissions.