  In this paper, we present a new cooperative communication scheme consisting
of two users in half-duplex mode communicating with one destination over a
discrete memoryless channel. The users encode messages in independent blocks
and divide the transmission of each block into 3 time slots with variable
durations. Cooperation is performed by partial decodeforward relaying over
these 3 time slots. During the first two time slots, each user alternatively
transmits and decodes, while during the last time slot, both users cooperate to
send information to the destination. An achievable rate region for this scheme
is derived using superposition encoding and joint maximum likelihood (ML)
decoding across the 3 time slots. An example of the Gaussian channel is treated
in detail and its achievable rate region is given explicitly. Results show that
the proposed half-duplex scheme achieves significantly larger rate region than
the classical multiple access channel and approaches the performance of a
full-duplex cooperative scheme as the inter-user channel quality increases.
