Semi-constrained Systems
Semi-constrained Systems
复制标题
半约束系统
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Ohad Elishco
中科院分区：
文献类型：
--
作者：
Moshe Schwartz;Tom Meyerovitch;Ohad Elishco
当通过噪声信道传输信息时，有两种常见的方法可以追溯到香农的工作：假设信道错误与传输内容无关并设计纠错码，或者假设错误与数据相关并设计一种约束编码方案来消除所有违规数据模式。在本文中，我们分析了一条中间道路，我们称之为半约束系统。在这样一个系统中，它是具有成本约束模型的通道的扩展，我们并没有完全消除引起错误的序列，而是限制它们出现的频率。
我们在这项研究中解决了几个关键问题。第一个是证明容量的封闭式界限，这使我们能够限制容量的渐进性。特别是，我们限制了随着 $k$ 的增长，半约束 $(0,k)$-RLL 的容量趋于 $1$ 的速率。第二个关键问题是设计有效的编码和解码程序，以渐进地实现容量且误差消失。最后，我们考虑涉及容量连续性和半约束系统定义放宽的微妙问题。
When transmitting information over a noisy channel, two approaches, dating back to Shannon's work, are common: assuming the channel errors are independent of the transmitted content and devising an error-correcting code, or assuming the errors are data dependent and devising a constrained-coding scheme that eliminates all offending data patterns. In this paper we analyze a middle road, which we call a semiconstrained system. In such a system, which is an extension of the channel with cost constraints model, we do not eliminate the error-causing sequences entirely, but rather restrict the frequency in which they appear.
We address several key issues in this study. The first is proving closed-form bounds on the capacity which allow us to bound the asymptotics of the capacity. In particular, we bound the rate at which the capacity of the semiconstrained $(0,k)$-RLL tends to $1$ as $k$ grows. The second key issue is devising efficient encoding and decoding procedures that asymptotically achieve capacity with vanishing error. Finally, we consider delicate issues involving the continuity of the capacity and a relaxation of the definition of semiconstrained systems.