  This work focuses on studying the half-duplex (HD) relaying in the Multiple
Access Relay Channel (MARC) and the Compound Multiple Access Channel with a
Relay (cMACr). A generalized Quantize-and-Forward (GQF) has been proposed to
establish the achievable rate regions. Such scheme is developed based on the
variation of the Quantize-and-Forward (QF) scheme and single block with two
slots coding structure. The results in this paper can also be considered as a
significant extension of the achievable rate region of Half-Duplex Relay
Channel (HDRC). Furthermore, the rate regions based on GQF scheme is extended
to the Gaussian channel case. The scheme performance is shown through some
numerical examples.
