Coding theorems for random access communication over compound channel

Random access communication is used in practical systems to deliver bursty short messages. Because users only transmit occasionally, it is often difficult for the receiver to keep track of the time varying wireless channel states. Under this motivation, we develop channel coding theorems for random multiple access communication over compound channels with finite codeword length. Error performance bound and asymptotic error probability scaling laws are derived. We found that the results also help in deriving error performance bounds for the random multiple access system where the receiver is only interested in decoding messages from a user subset.