Information transmission over a finite buffer channel

We study information transmission through a finite buffer channel modeled as a concatenation of a discrete memoryless channel (DMC) and a finite state erasure channel. The state of the erasure channel is determined by the buffer occupancy upon arrival of the transmission symbol; an erasure occurs when an input arrives to a full buffer. We show that the capacity of the channel depends on the long-term loss probability of the buffer and the capacity of the DMC. Thus, even though the channel itself has memory, the capacity apparently depends only on the stationary loss probability of the buffer. We also show that delayed feedback does not help in this channel. We also study the channel as a deletion channel where we do not know where the erasures have occurred.