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Optimal Design of Sequential Real-Time Communication Systems

机译：顺序实时通信系统的优化设计

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Optimal design of sequential real-time communication of a Markov source over a noisy channel is investigated. In such a system, the delay between the source output and its reconstruction at the receiver should equal a fixed prespecified amount. An optimal communication strategy must minimize the total expected symbol-by-symbol distortion between the source output and its reconstruction. Design techniques or performance bounds for such real-time communication systems are unknown. In this paper a systematic methodology, based on the concepts of information structures and information states, to search for an optimal real-time communication strategy is presented. This methodology trades off complexity in communication length (linear in contrast to doubly exponential) with complexity in alphabet sizes (doubly exponential in contrast to exponential). As the communication length is usually order of magnitudes bigger than the alphabet sizes, the proposed methodology simplifies the search for an optimal communication strategy. In spite of this simplification, the resultant optimality equations cannot be solved efficiently using existing algorithmic techniques. The main idea is to formulate a zero-delay communication problem as a dynamic team with nonclassical information structure. Then, an appropriate choice of information states converts the dynamic team problem into a centralized stochastic control problem in function space. Thereafter, Markov decision theory is used to derive nested optimality equations for choosing an optimal design. For infinite horizon problems, these optimality equations give rise to a fixed point functional equation. Communication systems with fixed finite delay constraint, a higher-order Markov source, and channels with memory are treated in the same manner after an appropriate expansion of the state space. Thus, this paper presents a comprehensive methodology to study different variations of real-time communication.
机译：研究了在有噪声信道上马尔可夫信号源的顺序实时通信的优化设计。在这样的系统中，源输出与其在接收机处的重构之间的延迟应等于固定的预定量。最佳的通信策略必须使源输出及其重构之间的总预期逐符号失真最小化。这种实时通信系统的设计技术或性能界限是未知的。本文提出了一种基于信息结构和信息状态概念的系统方法，以寻求最佳的实时通信策略。该方法权衡了通信长度的复杂度（与双指数相反的线性）和字母大小的复杂度（与指数相反的双指数）。由于通信长度通常比字母大小大几个数量级，因此所提出的方法简化了对最佳通信策略的搜索。尽管进行了这种简化，但是使用现有算法技术仍无法有效地求解所得最优方程。主要思想是将零延迟通信问题表述为具有非经典信息结构的动态团队。然后，对信息状态的适当选择将动态团队问题转换为功能空间中的集中式随机控制问题。此后，使用马尔可夫决策理论推导嵌套的最优方程，以选择最优设计。对于无限视界问题，这些最优方程产生了一个定点函数方程。在适当扩展状态空间之后，将以固定的有限延迟约束，高阶马尔可夫源和具有内存的通道的通信系统以相同的方式处理。因此，本文提出了一种综合的方法来研究实时通信的不同变化。

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