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We consider the information-theoretic optimality of treating inter-cellinterference as noise (multi-cell TIN) in downlink cellular networks. We focuson scenarios modeled by the Gaussian interfering broadcast channel (IBC),comprising $K$ mutually interfering Gaussian broadcast channels (BCs), eachformed by a base station communicating independent messages to an arbitrarynumber of users. We establish a new power allocation duality between the IBCand its dual interfering multiple access channel (IMAC), which entails that thecorresponding generalized degrees-of-freedom regions achieved throughmulti-cell TIN and power control (TINA regions) for both networks areidentical. As by-products of this duality, we obtain an explicitcharacterization of the IBC TINA region from a previously establishedcharacterization of the IMAC TINA region; and identify a multi-cell convex-TINregime in which the IBC TINA region is a polyhedron (hence convex) without theneed for time-sharing. We then identify a smaller multi-cell TIN regime inwhich the IBC TINA region is optimal and multi-cell TIN achieves the entirecapacity region of the IBC, up to a constant gap. This is accomplished byderiving a new genie-aided outer bound for the IBC, that reveals a novelBC-type order that holds amongst users in each constituent BC (or cell) underinter-cell interference, which in turn is not implied by previously knownBC-type orders (i.e. degraded, less noisy and more capable orders). Themulti-cell TIN regime that we identify for the IBC coincides with acorresponding multi-cell TIN regime previously identified for the IMAC, henceestablishing a comprehensive uplink-downlink duality of multi-cell TIN in theGDoF (and approximate capacity) sense.

On the Optimality of Treating Inter-Cell Interference as Noise: Downlink Cellular Networks and Uplink-Downlink Duality