The interest in channel models in which the data is sent as an unordered set of binary strings has increased lately, due to emerging applications in DNA storage, among others. In this paper we analyze the minimal redundancy of binary codes for this channel under substitution errors, and provide several constructions, some of which are shown to be asymptotically optimal up to constants. The surprising result in this paper is that while the information vector is sliced into a set of unordered strings, the amount of redundant bits that are required to correct errors is order-wise equivalent to the amount required in the classical error correcting paradigm.

中文翻译：

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关于对切片信息进行编码


最近，由于 DNA 存储等领域的新兴应用，人们对将数据作为一组无序二进制字符串发送的通道模型的兴趣有所增加。在本文中，我们分析了该通道在替换错误下的二进制码的最小冗余，并提供了几种结构，其中一些结构被证明在常数范围内是渐近最优的。本文中令人惊讶的结果是，虽然信息向量被分割成一组无序字符串，但纠正错误所需的冗余位数量按顺序相当于经典纠错范例中所需的数量。