Blahut–Arimoto Algorithms for Inner and Outer Bounds on Capacity Regions of Broadcast Channels
The celebrated Blahut–Arimoto algorithm computes the capacity of a discrete memoryless point-to-point channel by alternately maximizing the objective function of a maximization problem. This algorithm has been applied to degraded broadcast channels, in which the supporting hyperplanes of the capacit...
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| Format: | Article |
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MDPI AG
2024-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/26/3/178 |
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| author | Yanan Dou Yanqing Liu Xueyan Niu Bo Bai Wei Han Yanlin Geng |
| author_facet | Yanan Dou Yanqing Liu Xueyan Niu Bo Bai Wei Han Yanlin Geng |
| author_sort | Yanan Dou |
| collection | DOAJ |
| description | The celebrated Blahut–Arimoto algorithm computes the capacity of a discrete memoryless point-to-point channel by alternately maximizing the objective function of a maximization problem. This algorithm has been applied to degraded broadcast channels, in which the supporting hyperplanes of the capacity region are again cast as maximization problems. In this work, we consider general broadcast channels and extend this algorithm to compute inner and outer bounds on the capacity regions. Our main contributions are as follows: first, we show that the optimization problems are max–min problems and that the exchange of minimum and maximum holds; second, we design Blahut–Arimoto algorithms for the maximization part and gradient descent algorithms for the minimization part; third, we provide convergence analysis for both parts. Numerical experiments validate the effectiveness of our algorithms. |
| first_indexed | 2024-04-24T18:18:45Z |
| format | Article |
| id | doaj.art-117a29b090a641f3ae4438291b60ea80 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-24T18:18:45Z |
| publishDate | 2024-02-01 |
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| series | Entropy |
| spelling | doaj.art-117a29b090a641f3ae4438291b60ea802024-03-27T13:36:46ZengMDPI AGEntropy1099-43002024-02-0126317810.3390/e26030178Blahut–Arimoto Algorithms for Inner and Outer Bounds on Capacity Regions of Broadcast ChannelsYanan Dou0Yanqing Liu1Xueyan Niu2Bo Bai3Wei Han4Yanlin Geng5State Key Laboratory of ISN, Xidian University, Xi’an 710071, ChinaIT Operation Center, Bank of China, Beijing 100094, ChinaTheory Lab, Central Research Institute, 2012 Labs, Huawei Tech. Co., Ltd., Shatin, N.T., Hong Kong SAR, ChinaTheory Lab, Central Research Institute, 2012 Labs, Huawei Tech. Co., Ltd., Shatin, N.T., Hong Kong SAR, ChinaTheory Lab, Central Research Institute, 2012 Labs, Huawei Tech. Co., Ltd., Shatin, N.T., Hong Kong SAR, ChinaState Key Laboratory of ISN, Xidian University, Xi’an 710071, ChinaThe celebrated Blahut–Arimoto algorithm computes the capacity of a discrete memoryless point-to-point channel by alternately maximizing the objective function of a maximization problem. This algorithm has been applied to degraded broadcast channels, in which the supporting hyperplanes of the capacity region are again cast as maximization problems. In this work, we consider general broadcast channels and extend this algorithm to compute inner and outer bounds on the capacity regions. Our main contributions are as follows: first, we show that the optimization problems are max–min problems and that the exchange of minimum and maximum holds; second, we design Blahut–Arimoto algorithms for the maximization part and gradient descent algorithms for the minimization part; third, we provide convergence analysis for both parts. Numerical experiments validate the effectiveness of our algorithms.https://www.mdpi.com/1099-4300/26/3/178Blahut–Arimoto algorithmbroadcast channelcapacity regionsuperposition coding inner boundMarton’s inner boundUV outer bound |
| spellingShingle | Yanan Dou Yanqing Liu Xueyan Niu Bo Bai Wei Han Yanlin Geng Blahut–Arimoto Algorithms for Inner and Outer Bounds on Capacity Regions of Broadcast Channels Entropy Blahut–Arimoto algorithm broadcast channel capacity region superposition coding inner bound Marton’s inner bound UV outer bound |
| title | Blahut–Arimoto Algorithms for Inner and Outer Bounds on Capacity Regions of Broadcast Channels |
| title_full | Blahut–Arimoto Algorithms for Inner and Outer Bounds on Capacity Regions of Broadcast Channels |
| title_fullStr | Blahut–Arimoto Algorithms for Inner and Outer Bounds on Capacity Regions of Broadcast Channels |
| title_full_unstemmed | Blahut–Arimoto Algorithms for Inner and Outer Bounds on Capacity Regions of Broadcast Channels |
| title_short | Blahut–Arimoto Algorithms for Inner and Outer Bounds on Capacity Regions of Broadcast Channels |
| title_sort | blahut arimoto algorithms for inner and outer bounds on capacity regions of broadcast channels |
| topic | Blahut–Arimoto algorithm broadcast channel capacity region superposition coding inner bound Marton’s inner bound UV outer bound |
| url | https://www.mdpi.com/1099-4300/26/3/178 |
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