Semiconstrained systems
Semiconstrained systems
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半约束系统
DOI：
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发表时间：
2014
期刊：
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通讯作者：
Moshe Schwartz
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文献类型：
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作者：
Ohad Elishco;Tom Meyerovitch;Moshe Schwartz
在有噪声的信道上传输信息时，有两种常见的方法：假设信道错误独立于传输的内容并设计纠错码，或者假设错误依赖于数据并设计消除所有违规数据模式的约束编码方案。本文分析了一种中间路径，我们称之为半应变系统。在这种模型中，它是具有成本约束的信道的扩展，我们并没有完全消除导致错误的序列，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闭边界，它允许我们对容量的渐近性进行限定。特别地，我们限定了半应变(0,k)-RLL的容量随k的增长趋于1的速率。第二个关键问题是设计有效的编码和解码程序，使其逐渐达到具有消失错误的容量。最后，我们考虑涉及容量的连续性和半应变系统定义的松弛的微妙问题。
When transmitting information over a noisy channel, two approaches 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 model, which is an extension of the channel with cost constraints, 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.