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

Goldsmith, Andrea J. and Effros, Michelle (2001) The capacity region of broadcast channels with intersymbol interference and colored Gaussian noise. IEEE Transactions on Information Theory, 47 (1). pp. 219-240. ISSN 0018-9448.

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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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Additional Information:“© 2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Manuscript received September 16, 1998; revised December 1, 1999. The work of A. J. Goldsmith was supported by an ONR Young Investigator Award N00014-99-1-0698 and by an NSF CAREER Award NCR-9501452. The work of M. Effros was supported by an NSF CAREER Award MIP-9501977, a grant from the Powell Foundation, and donations from Intel. The authors gratefully acknowledge R. Gallager and R. Cheng for discussions on correlated noise, A. El Gamal for discussions on common information, and S. Shamai and J. Thomas for pointing out [8]. They are also grateful to the anonymous reviewers for their detailed suggestions and comments.
Subject Keywords:Broadcast channels, capacity region, colored Gaussian noise, intersymbol interference (ISI), network information theory, channel capacities
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Deposited On:08 Jan 2006
Last Modified:02 Oct 2019 22:41

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