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On the Achievable Rate Region of the K-Receiver Broadcast Channels via Exhaustive Message Splitting

by 1,2,3, 1,2,3 and 1,*
1
School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China
2
Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200083, China
3
University of Chinese Academy of Sciences, Beijing 100049, China
*
Author to whom correspondence should be addressed.
Academic Editor: Song-Nam Hong
Entropy 2021, 23(11), 1408; https://doi.org/10.3390/e23111408
Received: 10 September 2021 / Revised: 9 October 2021 / Accepted: 18 October 2021 / Published: 26 October 2021
(This article belongs to the Section Information Theory, Probability and Statistics)
This paper focuses on K-receiver discrete-time memoryless broadcast channels (DM-BCs) with private messages, where the transmitter wishes to convey K private messages to K receivers. A general inner bound on the capacity region is proposed based on an exhaustive message splitting and a K-level modified Marton’s coding. The key idea is to split every message into j=1KKj1 submessages each corresponding to a set of users who are assigned to recover them, and then send these submessages via codewords chosen from a K-level structure codebooks. To guarantee the joint typicality among all transmitted codewords, a sufficient condition on the subcodebooks’ sizes is derived through a newly establishing hierarchical covering lemma, which extends the 2-level multivariate covering lemma to the K-level case with more intricate dependences. As the number of auxiliary random variables and rate conditions both increase exponentially with K, the standard Fourier–Motzkin elimination procedure becomes infeasible when K is large. To tackle this problem, we obtain a closed form of achievable rate region with a special observation of disjoint unions of sets that constitute the power set of {1,,K}. The proposed achievable rate region allows arbitrary input probability mass functions and improves over previously known achievable (closed form) rate regions for K-receiver (K3) BCs. View Full-Text
Keywords: broadcast channel; capacity region; covering lemma broadcast channel; capacity region; covering lemma
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MDPI and ACS Style

Tang, R.; Xie, S.; Wu, Y. On the Achievable Rate Region of the K-Receiver Broadcast Channels via Exhaustive Message Splitting. Entropy 2021, 23, 1408. https://doi.org/10.3390/e23111408

AMA Style

Tang R, Xie S, Wu Y. On the Achievable Rate Region of the K-Receiver Broadcast Channels via Exhaustive Message Splitting. Entropy. 2021; 23(11):1408. https://doi.org/10.3390/e23111408

Chicago/Turabian Style

Tang, Rui, Songjie Xie, and Youlong Wu. 2021. "On the Achievable Rate Region of the K-Receiver Broadcast Channels via Exhaustive Message Splitting" Entropy 23, no. 11: 1408. https://doi.org/10.3390/e23111408

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