The Kronecker space-time MIMO network code

We build upon [1] for the case of error-prone wireless access networks and transmission over finite fields. Our focus is the derivation of the network code naturally provided by the wireless topology when using packet-level channel coding. The topology is assumed to be an LxL Multiple Input Multiple Output (MIMO) and transmission units are q-ary row vectors. Our results include the following. First, our model algebraically decouples the effect of the network topology (occurring on the encoding spatial domain) from the effect of the packet-level channel coding (occurring on the time encoding domain). Second, the model algebraically matches space and time encoding domains with the network code coefficients provided by the physical layer, which are formalized as a natural space-time erasure channel. Third, the model yields an algebraic interpretation of network coding for unicast and multicast as weighted projections onto lower-dimensional subspaces. Finally, we analytically derive the space-time q-ary repetition code that the MIMO topology and the channel coding introduce. The Kronecker product is shown to be the natural way to express the encoding functions.