论文标题
反馈频道通信量低精度算术
Feedback Channel Communication with Low Precision Arithmetic
论文作者
论文摘要
考虑使用低精度算术在加性白色高斯噪声通道上通过加性白色高斯噪声通道进行交流的问题。已知Schalkwijk-kailath（SK）方案实现了一种误差概率，该误差概率在交互作用的数量中呈双重衰减，以低于通道容量的任何速率。但是，众所周知，SK遭受了数值问题。接近通道容量的传输需要中等数量的交互作用。这可能会导致巨大的星座大小。此外，方案衰减的内部变量呈指数快速为零。结果，使用低精度变量实现时，SK方案将失败，这些变量被广泛用于硬件实现。在这项工作中，我们提出了一种称为Zoom-In SK（ZSK）的新的，修改的方案，该方案将SK协议分为多个阶段。每个阶段都包括几个SK迭代，然后是同步缩放步骤。缩放允许接收器和发射器保持方案的参数相对较大，以便甚至可以使用很大的速率或大量的相互作用回合也可以使用低精度算术。我们证明，新方案的错误概率大致与SK的误差概率大致相同，而没有遇到数值问题。我们在模拟中进一步验证了我们的结果，并将ZSK与原始SK方案进行比较。
The problem of communicating over an additive white Gaussian noise channel with feedback, using low precision arithmetic, is considered. The Schalkwijk-Kailath (SK) scheme is known to achieve an error probability that decays double exponentially in the number of interaction rounds, for any rate below channel capacity. However, SK is also known to suffer from numerical issues. Transmission close to channel capacity requires a moderate number of interaction rounds. This may lead to a huge constellation size. Furthermore, the internal variables of the scheme decay to zero exponentially fast. As a result, the SK scheme fails when implemented with low precision variables, which are widely used in hardware implementations. In this work we propose a new, modified scheme termed Zoom-in SK (ZSK), which breaks the SK protocol into several stages. Each stage comprises several SK iterations followed by a synchronized zoom step. The zoom-in allows the receiver and transmitter to keep the scheme's parameters relatively large such that low precision arithmetic can be used even for a large rate or a large number of interaction rounds. We prove that the new scheme achieves approximately the same error probability as SK while not suffering from numerical issues. We further verify our results in simulation and compare ZSK to the original SK scheme.
