  We investigate optimal routing and scheduling strategies for multi-hop
wireless networks with rateless codes. Rateless codes allow each node of the
network to accumulate mutual information from every packet transmission. This
enables a significant performance gain over conventional shortest path routing.
Further, it outperforms cooperative communication techniques that are based on
energy accumulation. However, it requires complex and combinatorial networking
decisions concerning which nodes participate in transmission, and which decode
ordering to use. We formulate three problems of interest in this setting: (i)
minimum delay routing, (ii) minimum energy routing subject to delay constraint,
and (iii) minimum delay broadcast. All of these are hard combinatorial
optimization problems and we make use of several structural properties of their
optimal solutions to simplify the problems and derive optimal greedy
algorithms. Although the reduced problems still have exponential complexity,
unlike prior works on such problems, our greedy algorithms are simple to use
and do not require solving any linear programs. Further, using the insight
obtained from the optimal solution to a line network, we propose two simple
heuristics that can be implemented in polynomial time and in a distributed
fashion and compare them with the optimal solution. Simulations suggest that
both heuristics perform very close to the optimal solution over random network
topologies.
