  Current medium access control mechanisms are based on collision avoidance and
collided packets are discarded. The recent work on ZigZag decoding departs from
this approach by recovering the original packets from multiple collisions. In
this paper, we present an algebraic representation of collisions which allows
us to view each collision as a linear combination of the original packets. The
transmitted, colliding packets may themselves be a coded version of the
original packets.
  We propose a new acknowledgment (ACK) mechanism for collisions based on the
idea that if a set of packets collide, the receiver can afford to ACK exactly
one of them and still decode all the packets eventually. We analytically
compare delay and throughput performance of such collision recovery schemes
with other collision avoidance approaches in the context of a single hop
wireless erasure network. In the multiple receiver case, the broadcast
constraint calls for combining collision recovery methods with network coding
across packets at the sender. From the delay perspective, our scheme, without
any coordination, outperforms not only a ALOHA-type random access mechanisms,
but also centralized scheduling. For the case of streaming arrivals, we propose
a priority-based ACK mechanism and show that its stability region coincides
with the cut-set bound of the packet erasure network.
