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Decoding mixed errors and erasures in permutation codes

机译：解码置换码中的混合错误和擦除

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摘要

Permutation codes have been studied because of a potential application to pow-erline communication. Efficient decoding in this application requires the existence of some structure in the permutation code. Many of the largest permutation codes known are unions of cosets of a nontrivial permutation group, and it is these codes that are the main subject of this paper. In the case when the code consists of a single permutation group, Bailey has developed an efficient method of decoding when the received word is affected by errors. This work is extended in three ways in this paper. Firstly, it is observed that the types of error occurring on a powerline channel lead to a mixture of errors and erasures. Further, some of the erasures may have an associated small candidate list of possible values, providing more information than simply treating them as erasures. Bailey's algorithm is modified to deal with mixtures of errors, erasures and candidate lists. Secondly, the algorithm is extended to codes which are unions of cosets of a group code. Thirdly, it is observed that using nearest neighbour decoding it is often possible to uniquely decode received words beyond the guaranteed capability of the code given by its minimum distance. Extra information may be available in candidate lists, and it is shown how this can aid decoding.
机译：由于置换代码在电力线通信中的潜在应用，因此已经对其进行了研究。在该应用中的有效解码要求置换码中存在某种结构。许多已知的最大置换码是非平凡置换组的陪集的并集，而这些码是本文的主要主题。在代码由单个排列组组成的情况下，Bailey开发了一种有效的方法来解码接收到的字受错误影响的情况。本文以三种方式扩展了这项工作。首先，观察到在电力线信道上发生的错误类型导致错误和擦除的混合。此外，某些擦除可能具有关联的可能值的较小候选列表，与简单地将其视为擦除相比，它提供了更多的信息。修改了Bailey的算法，以处理错误，擦除和候选列表的混合体。其次，该算法被扩展到作为组代码的陪集的并集的代码。第三，观察到，使用最近邻居解码，通常有可能对接收到的单词进行唯一解码，而超出了其最小距离所给出的代码的保证能力。候选列表中可能会提供其他信息，并显示了如何帮助解码。

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