Markov chain analysis of collaborative codes in random multi access communication systems

A discrete-time Markov chain analysis is developed for the performance of collaborative codes in random multi access communication systems (CCMA). Two media access schemes are proposed: asynchronous CCMA where users can start transmission at any time and synchronous CCMA where users can start transmission only at the start of a synchronizing clock. The performance of these two systems is compared with pure ALOHA and slotted ALOHA, respectively. It is shown that these well-known protocols are special case of CCMA when the number of available codes is only one. The performance of 2-, 3-, and 5-user codes is studied and it is shown that they offer significant performance enhancement in CCMA environment compared to the non-coded case in terms of throughput, efficiency, delay, and the number of retries for a successful transmission. Because of CCMA advantages, their use for voice traffic application is studied and it was found that CCMA allows more traffic than the non-coded case for all codes used, which is doubled in the case of 5-user slotted environment.