  This paper provides comprehensive coding and outer bound for the half-duplex
multiple access channel with generalized feedback (MAC-GF). Two users
communicate with one destination over a discrete memoryless channel using time
division. Each transmission block is divided into 3 time slots with variable
durations: the destination is always in receive mode, while each user
alternatively transmits and receives during the first 2 time slots, then both
cooperate to send information during the last one. The paper proposes two
decode-forward based coding schemes, analyzes their rate regions, and also
derives two outer bounds with rate constraints similar to the achievable
regions. Both schemes requires no block Makovity, allowing the destination to
decode at the end of each block without any delay. In the first scheme, the
codewords in the third time slot are superimposed on the codewords of the first
two, whereas in the second scheme, these codewords are independent. While the
second scheme is simpler, the first scheme helps emphasize the importance of
joint decoding over separate decoding among multiple time slots at the
destination. For the Gaussian channel, the two schemes with joint decoding are
equivalent, as are the two outer bounds. For physically degraded Gaussian
channels, the proposed schemes achieve the capacity. Extension to the m-user
half-duplex MAC-GF are provided. Numerical results for the Gaussian channel
shows significant rate region improvement over the classical MAC and that the
outer bound becomes increasingly tight as the inter-user link quality increases
