  The state-dependent $K$-user memoryless Broadcast Channel~(BC) with state
feedback is investigated. We propose a novel transmission scheme and derive its
corresponding achievable rate region, which, compared to some general schemes
that deal with feedback, has the advantage of being relatively simple and thus
is easy to evaluate. In particular, it is shown that the capacity region of the
symmetric erasure BC with an arbitrary input alphabet size is achievable with
the proposed scheme. For the fading Gaussian BC, we derive a symmetric
achievable rate as a function of the signal-to-noise ratio~(SNR) and a small
set of parameters. Besides achieving the optimal degrees of freedom at high
SNR, the proposed scheme is shown, through numerical results, to outperform
existing schemes from the literature in the finite SNR regime.
