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首页> 外文期刊>Information Theory, IEEE Transactions on >Characteristic Generators and Dualization for Tail-Biting Trellises
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Characteristic Generators and Dualization for Tail-Biting Trellises

机译：咬尾格子的特征发生器和对偶化

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This paper focuses on dualizing tail-biting trellises, particularly KV trellises. These trellises are based on characteristic generators, as introduced by Koetter–Vardy (2003), and may be regarded as a natural generalization of minimal conventional trellises, even though they are not necessarily minimal. Two dualization techniques will be investigated: the local dualization, introduced by Forney (2001) for general normal graphs, and a linear-algebra-based dualization tailored to the specific class of tail-biting Bahl–Cocke–Jelinek–Raviv (BCJR) trellises, introduced by Nori–Shankar (2006). It turns out that, in general, the BCJR dual is a subtrellis of the local dual, while for KV trellises these two coincide. Furthermore, making use of both the BCJR construction and the local dualization, it will be shown that for each complete set of characteristic generators of a code there exists a complete set of characteristic generators of the dual code such that their resulting KV trellises are dual to each other if paired suitably. This proves a stronger version of a conjecture formulated by Koetter–Vardy.
机译：本文着重于对咬尾格网，特别是KV格网进行二元化。这些网格基于Koetter–Vardy（2003）引入的特征生成器，即使未必是最小的，也可以看作是最小常规网格的自然概括。将研究两种双重化技术：Forney（2001）针对一般正态图引入的局部双重化，以及针对特定类型的咬尾Bahl-Cocke-Jelinek-Raviv（BCJR）格网量身定制的基于线性代数的双重化，由Nori–Shankar（2006）引入。事实证明，一般而言，BCJR对偶是局部对偶的子格，而对于KV格，这两个格是重合的。此外，利用BCJR构造和局部对偶化，将显示出，对于每个完整的代码特征生成器集，都存在完整的对偶代码特征生成器集，从而它们产生的KV格对彼此配对（如果配对正确）。这证明了Koetter-Vardy提出的猜想的更强形式。

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