Staircase codes are a class of high performance forward-error-correction codes for high-rate transmission and hard decision decoding. They are initially designed for high-rate fiber optic transmission, which intends to correct errors in binary symmetry channels. However, to apply these high performance high-rate codes on wireless channels, some other aspects require close attention, which are addressed in this work. Staircase codes for wireless transmissions on burst-error channels, which can be modelled using Gilbert and Elliott-s model, are investigated. The Staircase codes with Reed-Solomon codes, as component codes, are tested in random-error as well as burst-error channels with different burst lengths and bit error probabilities, and are compared with the baseline Staircase codes with binary Bose-Chaudhuri Hochquenghem (BCH) component codes. Furthermore Staircase codes with interleaving are implemented and tested in random-error, as well as burst-error channels with different burst lengths and bit error probabilities. For both types of component codes, the software complexities and decoding latencies are compared to see which codes have major impact on the decoding time of the Staircase codes. For time-variant wireless channels (both optical and RF), Staircase codes with adaptive rates are proposed and used in type-II hybrid ARQ frameworks, so that throughput is maximized by avoiding retransmissions of the whole Staircase blocks that initially - at high code rate - might not have been decoded successfully. These rate-adaptive Staircase codes employ at their core the standard BCH component codes, but they are concatenated with Reed-Solomon codes as extra components to implement burst-error correction and rate-adaptivity. Bit error performance and throughput of the rate-adaptive Staircase codes are investigated by analysis and confirmed with simulations. The possibility of using staircase codes in the framework of distributed source coding (DSC) is also investigated as a further potential application. The bit error Slepian-Wolf coding, which is the bit error from lossy source coding, and the rate curve of Slepian-Wolf coding using Staircase codes with BCH component codes to compress the data are obtained.