低精度算法的反馈通道通信
Feedback Channel Communication with Low Precision Arithmetic
摘要：
研究了在加性高斯白噪声信道中，采用低精度算法进行反馈通信的问题。对于低于信道容量的任何速率，已知Schalkwijk-Kailath（SK）方案实现了在交互循环数中双指数衰减的错误概率。然而，SK也被称为遭受数字问题。接近信道容量的传输需要中等数量的交互轮。这可能导致巨大的星座尺寸。此外，该方案的内部变量以指数速度衰减到零。因此，SK方案在用低精度变量实现时失败，低精度变量广泛用于硬件实现。在这项工作中，我们提出了一个新的，修改后的计划，称为放大SK（ZEAK），打破了SK协议分为几个阶段。每个阶段包括几个SK迭代，然后是同步缩放步骤。放大允许接收器和发射器保持方案的参数相对较大，使得即使对于大速率或大量交互循环也可以使用低精度算术。我们证明了新方案实现了与SK近似相同的错误概率，同时不存在数值问题。我们进一步验证了我们的结果在模拟和比较，原始SK方案的WARK。
英文摘要：
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.
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