论文标题
分散的顺序主动假设检验和MAC反馈能力
Decentralized sequential active hypothesis testing and the MAC feedback capacity
论文作者
论文摘要
我们考虑分散的顺序主动假设检验（DSAHT）的问题，其中两个具有私人信息的传输代理正在积极帮助第三个代理 - 彼此之间 - 通过离散的无内存多访问通道（DM-MAC）学习消息对。第三代理（接收器）观察嘈杂的通道输出，该输出也可以通过无噪声反馈来传输代理。我们将此问题提出为分散的动态团队，表明最佳传输策略具有时间不变的域，并通过动态程序来表征解决方案。讨论了几种涉及时间基础成本函数和/或可变长度代码的替代公式，从而通过定点，贝尔曼型方程描述了解决方案。 随后，我们与简化DM-MAC无噪声反馈能力的多字母能力表达式的问题建立了联系。我们表明，限制了对DSAHT问题最佳传输方案引起的分布的关注，而不会丧失最佳性，从而改变了容量表达，因此可以将其视为具有适当定义的随机动力学系统带有时间不变状态空间的平均奖励。
We consider the problem of decentralized sequential active hypothesis testing (DSAHT), where two transmitting agents, each possessing a private message, are actively helping a third agent--and each other--to learn the message pair over a discrete memoryless multiple access channel (DM-MAC). The third agent (receiver) observes the noisy channel output, which is also available to the transmitting agents via noiseless feedback. We formulate this problem as a decentralized dynamic team, show that optimal transmission policies have a time-invariant domain, and characterize the solution through a dynamic program. Several alternative formulations are discussed involving time-homogenous cost functions and/or variable-length codes, resulting in solutions described through fixed-point, Bellman-type equations. Subsequently, we make connections with the problem of simplifying the multi-letter capacity expressions for the noiseless feedback capacity of the DM-MAC. We show that restricting attention to distributions induced by optimal transmission schemes for the DSAHT problem, without loss of optimality, transforms the capacity expression, so that it can be thought of as the average reward received by an appropriately defined stochastic dynamical system with time-invariant state space.
