具有限制错误集的码的最小化字母表长度
Minimizing the alphabet size in codes with restricted error sets
摘要：
本文重点介绍了纠错码，可以处理一组预定义的特定错误模式。在包括无线通信和闪存系统的许多实际感兴趣的设置中出现了对这种代码的需要。在许多这样的设置中，可以实现比MDS和其他标准码所提供的更小的字段大小。我们建立了一个连接的最小字母表的大小为这个广义的设置和组合性质的超图，代表了预先指定的错误模式的集合。我们还显示了错误和纠删码在这个专门的设置之间的连接。这使我们能够建立界限上的最小字母表的大小，并显示出优势的非线性代码的线性代码在一个广义的设置。我们还考虑了一个变化的问题，它允许一个小概率的解码错误，并将其与超图着色的近似版本。
英文摘要：
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In many such settings, a smaller field size is achievable than that offered by MDS and other standard codes. We establish a connection between the minimum alphabet size for this generalized setting and the combinatorial properties of a hypergraph that represents the prespecified collection of error patterns. We also show a connection between error and erasure correcting codes in this specialized setting. This allows us to establish bounds on the minimum alphabet size and show an advantage of non-linear codes over linear codes in a generalized setting. We also consider a variation of the problem which allows a small probability of decoding error and relate it to an approximate version of hypergraph coloring.
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