The capacity region of broadcast channels with intersymbol interference and colored Gaussian noise

We derive the capacity region for a broadcast channel,vith intersymbol inte rference (ISI) and colored Gaussian noise under an input power constraint. The region is obtained by first defining a similar channel model, the circu lar broadcast channel, which can be decomposed into a set of parallel degra ded broadcast channels. The capacity region for parallel degraded broadcast channels is known. We then show that the capacity region of the original b roadcast channel equals that of the circular broadcast channel in the limit of infinite block length, and we obtain an explicit formula for the result ing capacity region, The coding strategy used to achieve each point on the convex hull of the capacity region uses superposition coding on some or all of the parallel channels and dedicated transmission on the others. The opt imal power allocation for any point in the capacity region is obtained via a multilevel water-filling. We derive this optimal power allocation and the resulting capacity region for several broadcast channel models.