  The Slepian-Wolf (SW) coding system is a source coding system with two
encoders and a decoder, where these encoders independently encode source
sequences from two correlated sources into codewords, and the decoder
reconstructs both source sequences from the codewords. In this paper, we
consider the situation in which the SW coding system is asynchronous, i.e.,
each encoder samples a source sequence with some unknown delay. We assume that
delays are unknown but maximum and minimum values of possible delays are known
to encoders and the decoder. We also assume that sources are discrete
stationary memoryless and the probability mass function (PMF) of the sources is
unknown but the system knows that it belongs to a certain set of PMFs. For this
asynchronous SW coding system, we clarify the achievable rate region which is
the set of rate pairs of encoders such that the decoding error probability
vanishes as the blocklength tends to infinity. We show that this region does
not always coincide with that of the synchronous SW coding system in which each
encoder samples a source sequence without any delay.
