In this paper, we aim to develop scheduling policies to maximize the stability region of a wireless network under the assumption that mutual information accumulation is implemented at the physical layer. This enhanced physical layer capability enables the system to accumulate information even when the link between two nodes is not good and a packet cannot be decoded within a slot. The result is an expansion of the stability region of the system. The accumulation process does not satisfy the i.i.d assumption that underlies many previous analysis in this area. Therefore it also brings new challenges to the problem. We propose two dynamic scheduling algorithms to overcome this difficulty. One performs scheduling every T slot, which inevitably increases average delay in the system, but approaches the boundary of the stability region. The second constructs a virtual system with the same stability region. Through controlling the virtual queues in the constructed system, we avoid the non-i.i.d difficulty and attain the stability region. We derive performance bounds under both algorithms and compare them through simulation results.