论文标题
部分可观测时空混沌系统的无模型预测
On the Performance of Reed-Muller Codes Over $(d,\infty)$-RLL Input-Constrained BMS Channels
论文作者
论文摘要
本文认为没有反馈的输入约束的二进制无内存对称（BMS）通道。频道输入序列尊重$（d，\ infty）$ - 运行limite Limited（RLL）约束，该约束要求将任何一对连续的$ 1 $ S分开至少$ d $ 0 $ s。我们考虑为此类渠道设计明确代码的问题。特别是，我们与Reed-Muller（RM）代码家族一起工作，Reeves和Pfister（2021）在位图解码下显示了任何无约束的BMS通道的容量。 We show that it is possible to pick $(d,\infty)$-RLL subcodes of a capacity-achieving (over the unconstrained BMS channel) sequence of RM codes such that the subcodes achieve, under bit-MAP decoding, rates of $C\cdot{2^{-\left \lceil \log_2(d+1)\right \rceil}}$, where $C$ is BMS通道的容量。最后，我们还引入了用于上限的技术，以将RM代码的特定能力调整序列的任何$（1，\ infty）$ - RLL子代码。
This paper considers the input-constrained binary memoryless symmetric (BMS) channel, without feedback. The channel input sequence respects the $(d,\infty)$-runlength limited (RLL) constraint, which mandates that any pair of successive $1$s be separated by at least $d$ $0$s. We consider the problem of designing explicit codes for such channels. In particular, we work with the Reed-Muller (RM) family of codes, which were shown by Reeves and Pfister (2021) to achieve the capacity of any unconstrained BMS channel, under bit-MAP decoding. We show that it is possible to pick $(d,\infty)$-RLL subcodes of a capacity-achieving (over the unconstrained BMS channel) sequence of RM codes such that the subcodes achieve, under bit-MAP decoding, rates of $C\cdot{2^{-\left \lceil \log_2(d+1)\right \rceil}}$, where $C$ is the capacity of the BMS channel. Finally, we also introduce techniques for upper bounding the rate of any $(1,\infty)$-RLL subcode of a specific capacity-achieving sequence of RM codes.
