论文标题
在线性 - 季度高斯控制中具有可变长度源编码的较低限制，并具有共同的随机性
A Lower-bound for Variable-length Source Coding in Linear-Quadratic-Gaussian Control with Shared Randomness
论文作者
论文摘要
在这封信中，我们考虑了一个线性二次高斯（LQG）控制系统，其中反馈在无噪声的二进制通道上发生，并在最低通信成本（通过通道比特量进行量化）中得出下限，以达到给定的控制性能。我们假设在每次步骤中，编码器都可以将包含可变数量的位置的数据包传达给控制器的解码器。我们的系统模型提供了编码器和解码器具有共享随机性的可能性，就像使用抖动量化器的系统中一样。我们定义了可能在消息包上施加的两个极端前缀要求；这样的限制很有用，因为它们允许解码器和其他代理商以在线方式唯一地识别传输的终结。然后，我们根据有指示信息得出了无前缀编码率的下限；特别是我们表明，以前已知的界限仍然具有共同的随机性。我们概括了何时放松前缀约束时的约束，并以速度延伸公式结论。
In this letter, we consider a Linear Quadratic Gaussian (LQG) control system where feedback occurs over a noiseless binary channel and derive lower bounds on the minimum communication cost (quantified via the channel bitrate) required to attain a given control performance. We assume that at every time step an encoder can convey a packet containing a variable number of bits over the channel to a decoder at the controller. Our system model provides for the possibility that the encoder and decoder have shared randomness, as is the case in systems using dithered quantizers. We define two extremal prefix-free requirements that may be imposed on the message packets; such constraints are useful in that they allow the decoder, and potentially other agents to uniquely identify the end of a transmission in an online fashion. We then derive a lower bound on the rate of prefix-free coding in terms of directed information; in particular we show that a previously known bound still holds in the case with shared randomness. We generalize the bound for when prefix constraints are relaxed, and conclude with a rate-distortion formulation.
