Is interference like noise when you know its codebook?

We consider a point to point communication system facing interference from other systems, with a particular focus on the case when this interference is undecodable. It is well known that when the interference is non-interactive, we can certainly treat it as additional noise at the receiver and thereby achieve certain rates. This paper asks whether any higher rates could be achieved by exploiting knowledge of the interferer's codebook. The main contribution of this paper is to study the converse: if the interference is undecodable, then we cannot do better than treating it as additional noise. This is proved for almost all interference codebooks when viewed under the random Gaussian codebook measure. When the interference signal is strong enough to be decodable, then codebook knowledge can be exploited at our receiver to allow higher rates to be achieved by appropriately structuring our own codebooks. Finally, we give an example of an interference codebook that cannot be completely decoded, but whose knowledge is still useful. However, this interference codebook is bad from the perspective of the interferer's own communication system. This leads us to conjecture that when the interference signal is undecodable, the only interference codebooks worth knowing are those that are not worth using from the interfering system's point of view