An Information Inequality and Evaluation of Marton's Inner Bound for Binary Input Broadcast Channels

• Published in: IEEE transactions on information theory Vol. 59; no. 7; pp. 4095 - 4105
• Main Authors: Yanlin Geng, Jog, V., Nair, C., Wang, Z. V.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-07-2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Binary input alphabet; Broadcasting; Broadcasting. Videocommunications. Audiovisual; Channel coding; Cramer-Rao bounds; Educational institutions; Entropy; Exact sciences and technology; information inequality; Information theory; Information, signal and communications theory; Markov processes; Marton's inner bound; Miscellaneous; Random variables; Receivers; Telecommunications; Telecommunications and information theory; Alphabet; Binary channel; Asymmetry; Marton's inner bound; Two channel system; Broadcast channels; information inequality; Binary input alphabet; Random variable
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2013.2253511

We establish an information inequality concerning five random variables. This inequality is motivated by the sum-rate evaluation of Marton's inner bound for two receiver broadcast channels with a binary input alphabet. We establish that randomized time-division strategy achieves the sum rate of Marton's inner bound for all binary input broadcast channels. We also obtain an improved cardinality bound for evaluating the maximum sum rate given by Marton's inner bound for all broadcast channels. Using these tools we explicitly evaluate the inner and outer bounds for the binary skew-symmetric broadcast channel and demonstrate a gap between the bounds.