Splitting algorithms in noisy channels with memory

Multiaccess networks in which the shared channel is noisy are considered. A slotted-time collision-type channel, Poisson infinite-user model, and a ternary feedback are assumed. Due to the noise in the shared channel, the received signal may be detected as a collision event though no message or a single message is transmitted. This kind of imperfect feedback is referred to as an error. A common assumption in all previous studies of multiaccess algorithms in channels with errors is that the channel is memoryless. The problem of splitting algorithms when the channel is with memory is considered here. A two-state first-order Markovian model for the channel is introduced and the operation of the tree collision resolution algorithm in this channel is analyzed. A stability result, i.e. the necessary conditions on the channel parameters for stability conditions hold, the throughput of the algorithm is calculated. Extensions to more general channel models are discussed