Even symmetric parallel linear deterministic interference channels are inseparable

It is well known that parallel interference channels (ICs) are in general inseparable. Existing results illustrate the benefit of joint encoding across sub-channels by exploiting the asymmetry within the individual sub-channels. In this paper, we show, perhaps surprisingly, that symmetric parallel ICs are also inseparable. To this end, a class of parallel ICs is considered in which each individual sub-channel is a symmetric linear deterministic IC (LDIC). The capacity region of this class of parallel ICs is characterized. As a consequence, we find the necessary and sufficient conditions for inseparability of this class of parallel ICs.