  We propose a new coding scheme for the discrete memoryless two-user
multi-access channel (MAC) with rate-limited feedback. Our scheme combines
ideas from the Venkataramanan-Pradhan scheme for perfect feedback with ideas
from the Shaviv-Steinberg scheme for rate-limited feedback.
  Our achievable region includes the Shaviv-Steinberg achievable region and
this inclusion can be strict. For general MACs and for sufficiently large
feedback rates, our scheme outperforms the Shaviv-Steinberg scheme as it
achieves the same rate region as the Venkataramanan-Pradhan scheme for perfect
feedback (which cannot be achieved by the Shaviv-Steinberg scheme).
Furthermore, we numerically evaluate our achievable region with a specific
(Gaussian) choice of random variables for the memoryless two-user Gaussian MAC.
Our simulation results show that for some parameters of the Gaussian MAC and
the feedback rate, our scheme achieves a strictly larger sum-rate than the
Shaviv-Steinberg scheme.
