  Scheduling to avoid packet collisions is a long-standing challenge in
networking, and has become even trickier in wireless networks with multiple
senders and multiple receivers. In fact, researchers have proved that even {\em
perfect} scheduling can only achieve $\mathbf{R} = O(\frac{1}{\ln N})$. Here
$N$ is the number of nodes in the network, and $\mathbf{R}$ is the {\em medium
utilization rate}. Ideally, one would hope to achieve $\mathbf{R} = \Theta(1)$,
while avoiding all the complexities in scheduling. To this end, this paper
proposes {\em cross-sender bit-mixing coding} ({\em BMC}), which does not rely
on scheduling. Instead, users transmit simultaneously on suitably-chosen slots,
and the amount of overlap in different user's slots is controlled via coding.
We prove that in all possible network topologies, using BMC enables us to
achieve $\mathbf{R}=\Theta(1)$. We also prove that the space and time
complexities of BMC encoding/decoding are all low-order polynomials.
