Characterization of graph-cover pseudocodewords of codes over F3

Vitaly Skachek
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引用次数: 9

Abstract

Linear-programming pseudocodewords play a pivotal role in our understanding of the linear-programming decoding algorithms. These pseudocodewords are known to be equivalent to the graph-cover pseudocodewords. The latter pseudocodewords, when viewed as points in the multidimensional Euclidean space, lie inside a fundamental cone. This fundamental cone depends on the choice of a parity-check matrix of a code, rather than on the choice of the code itself. The cone does not depend on the channel, over which the code is employed. The knowledge of the boundaries of the fundamental cone could help in studying various properties of the pseudocodewords, such as their minimum pseudoweight, pseudoredundancy of the codes, etc. For the binary codes, the full characterization of the fundamental cone was derived by Koetter et al. However, if the underlying alphabet is large, such characterization becomes more involved. In this work, a characterization of the fundamental cone for codes over F3 is discussed.
F3上码的图盖伪码字的表征
线性规划伪码字在理解线性规划译码算法中起着至关重要的作用。已知这些伪码字与图盖伪码字等效。后一种伪码字,当被视为多维欧几里得空间中的点时,位于一个基本锥体内。这个基本锥取决于码的奇偶校验矩阵的选择,而不是码本身的选择。锥形不依赖于使用代码的信道。了解基锥的边界有助于研究伪码字的各种性质,如伪码的最小伪权、伪冗余等。对于二进制码,由Koetter等人导出了基锥的完整表征。然而,如果潜在的字母表很大,这种特征就会变得更加复杂。在这项工作中,讨论了F3上码的基本锥的特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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