The Capacity Region of a Product of Two Unmatched Physically Degraded Gaussian Broadcast Channels With Three Individual Messages and a Common Message

• Published in: IEEE transactions on information theory Vol. 59; no. 1; pp. 76 - 103
• Main Authors: Gohary, R. H., Davidson, T. N.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-01-2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Broadcast channels with physically degraded components; Broadcasting; Broadcasting. Videocommunications. Audiovisual; Channels; Codes; Coding; Coding, codes; Decoding; Degradation; Encoding; entropy power inequality; Exact sciences and technology; Gaussian; geometric programming; Information theory; Information, signal and communications theory; Karush-Kuhn-Tucker (KKT) conditions; Messages; MIMO; Miscellaneous; Normal distribution; Receivers; relaxation; Signal and communications theory; superposition coding (SPC); Switching and signalling; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmitters; Vectors; Relaxation; entropy power inequality; Gaussian channel; Broadcast channels; Broadcast channels with physically degraded components; geometric programming; Entropy; superposition coding (SPC); Signalling; Channel coding; Karush-Kuhn-Tucker (KKT) conditions
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2012.2219172

This paper considers a Gaussian broadcast channel with two unmatched degraded components, three individual messages, and a common message that is intended for all three receivers. It is shown that for this channel, superposition coding with Gaussian signalling is sufficient to achieve every point in the capacity region.