Parallel linear deterministic interference channels with feedback: Combinatorial structure and separability

The sum-capacity of a 2-user linear deterministic interference channel (LDIC) can always be achieved with simple deterministic codes. The existence and design of such codes has been shown to be related to an underlying combinatorial structure of the channel. This is used here to explore the capacity of parallel or ergodic LDICs and LDICs with output feedback. We present simple algorithms that generate sum-rate optimal schemes in these cases. In the case of parallel LDICs this approach gives insight into when the channels are separable, i.e. when coding over component channels is not required. We further demonstrate that output feedback can change the separability of such channels.