The capacity region of broadcast channels with intersymbolinterference and colored Gaussian noise
Goldsmith, A.J.; Effros, M.
Information Theory, IEEE Transactions on
Volume 47, Issue 1, Jan 2001 Page(s):219 - 240
Digital Object Identifier 10.1109/18.904524
Summary:We derive the capacity region for a broadcast channel with
intersymbol interference (ISI) and colored Gaussian noise under an input
power constraint. The region is obtained by first defining a similar
channel model, the circular broadcast channel, which can be decomposed
into a set of parallel degraded broadcast channels. The capacity region
for parallel degraded broadcast channels is known. We then show that the
capacity region of the original broadcast channel equals that of the
circular broadcast channel in the limit of infinite block length, and we
obtain an explicit formula for the resulting 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 optimal 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
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