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首页> 外文会议>International Castle Meeting on Coding Theory and Applications >Minimal Trellis Construction for Finite Support Convolutional Ring Codes
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Minimal Trellis Construction for Finite Support Convolutional Ring Codes

机译：有限支撑卷积环码的最小网格施工

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摘要

We address the concept of "minimal polynomial encoder" for finite support linear convolutional codes over Z{sub}(p{sup}r). These codes can be interpreted as polynomial modules which enables us to apply results from the 2007-paper [8] to introduce the notions of "p-encoder" and "minimal p-encoder". Here the latter notion is the ring analogon of a row reduced polynomial encoder from the field case. We show how to construct a minimal trellis representation of a delay-free finite support convolutional code from a minimal p-encoder. We express its number of trellis states in terms of a degree invariant of the code. The latter expression generalizes the wellknown expression in terms of the degree of a delay-free finite support convolutional code over a field to the ring case. The results are also applicable to block trellis realization of polynomial block codes over Z{sub}(p{sup}r), such as CRC codes over Z{sub}(p{sup}r).
机译：我们通过z {sub}（p {sup} r）来解决有限支撑线性卷积码的“最小多项式编码器”的概念。这些代码可以解释为多项式模块，这使我们能够应用于2007纸[8]的结果，以介绍“p-encoder”和“最小p-encoder”的概念。在这里，后一概念是从场壳体的行减少的多项式编码器的环形模拟。我们展示了如何从最小的P-encoder构建无延迟有限支持卷积码的最小网格表示。我们在代码的程度不变的方面表达了Trellis状态的数量。后一表达在圆形壳体上的无延迟有限支撑卷积规范方面概括了众所周知的表达。结果也适用于阻止Trellis在z {sub}（p {sup} r）上的多项式块代码的实现，例如通过z {sub}的CRC代码（p {sup} r）。

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