Dou Yanan, Liu Yanqing, Niu Xueyan, Bai Bo, Han Wei, Geng Yanlin
State Key Laboratory of ISN, Xidian University, Xi'an 710071, China.
IT Operation Center, Bank of China, Beijing 100094, China.
Entropy (Basel). 2024 Feb 20;26(3):178. doi: 10.3390/e26030178.
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.
著名的Blahut-Arimoto算法通过交替最大化一个最大化问题的目标函数来计算离散无记忆点对点信道的容量。该算法已应用于降级广播信道，其中容量区域的支撑超平面同样被转化为最大化问题。在这项工作中，我们考虑一般的广播信道，并扩展该算法以计算容量区域的内界和外界。我们的主要贡献如下：第一，我们表明优化问题是极大极小问题，并且最小和最大的交换成立；第二，我们为最大化部分设计了Blahut-Arimoto算法，为最小化部分设计了梯度下降算法；第三，我们为这两部分提供了收敛性分析。数值实验验证了我们算法的有效性。
