半约束系统
Semi-constrained Systems
摘要：
当在有噪声的信道上传输信息时，有两种方法，可以追溯到香农的工作，是常见的：假设信道错误与传输的内容无关，并设计一个纠错码，或者假设错误是数据相关的，并设计一个约束编码方案，消除所有的违规数据模式。在本文中，我们分析了一个中间道路，我们称之为一个应变系统。在这样的系统中，这是一个扩展的信道与成本约束模型，我们不完全消除的错误引起的序列，而是限制它们出现的频率。我们在这项研究中解决几个关键问题。第一个是证明封闭形式的能力，使我们能够绑定的能力的渐近界。特别地，我们限制了当$k$增长时，应变的$(0,k)$ -RLL的容量趋向于$1$的速率。第二个关键问题是设计有效的编码和解码过程，渐近实现容量与消失的错误。最后，我们考虑微妙的问题，涉及的连续性的能力和放松的定义的超应变系统。
英文摘要：
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.
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