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首页> 外文期刊>Information Theory, IEEE Transactions on >Codes on Graphs: Duality and MacWilliams Identities
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Codes on Graphs: Duality and MacWilliams Identities

机译：图上的代码：对偶和MacWilliams身份

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摘要

A conceptual framework involving partition functions of normal factor graphs is introduced, paralleling a similar recent development by Al-Bashabsheh and Mao. The partition functions of dual normal factor graphs are shown to be a Fourier transform pair, whether or not the graphs have cycles. The original normal graph duality theorem follows as a corollary. Within this framework, MacWilliams identities are found for various local and global weight generating functions of general group or linear codes on graphs; this generalizes and provides a concise proof of the MacWilliams identity for linear time-invariant convolutional codes that was recently found by Gluesing-Luerssen and Schneider. Further MacWilliams identities are developed for terminated convolutional codes, particularly for tail-biting codes, similar to those studied recently by Bocharova, Hug, Johannesson, and Kudryashov.
机译：引入了涉及正态因子图的分区函数的概念框架，并与Al-Bashabsheh和Mao的类似最新发展相平行。对偶正态因子图的分区函数显示为傅立叶变换对，无论这些图是否具有周期。原始的正态图对偶定理是推论。在此框架内，可以找到MacWilliams身份，用于图上一般组或线性代码的各种局部和全局权重生成函数；这概括并提供了Gluesing-Luerssen和Schneider最近发现的线性时不变卷积码MacWilliams身份的简明证明。进一步的MacWilliams身份被开发用于终止的卷积码，尤其是用于咬尾码，类似于Bocharova，Hug，Johannesson和Kudryashov最近研究的那些。

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