Connections between linear systems and convolutional codes
Connections between linear systems and convolutional codes
复制标题
线性系统和卷积码之间的联系
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
J. Rosenthal
中科院分区：
文献类型：
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作者：
J. Rosenthal
文章回顾了可以在文献中找到的卷积码的不同定义。详细地计算了定义之间的代数差异。证明了双无限支撑系统在Pontryagin对偶下是有限支撑系统的对偶。在这种对偶中，可控系统的对偶是可观测的，反之亦然。只有当行为中存在双无限支承轨迹时，才可能发生不可控性，因此有限支承和半无限支承系统必须是可控的。只有当行为中存在有限支撑轨迹时，才可能发生不可观测性，因此双无限和半无限支撑系统必须是可观测的。它表明，卷积码的不同定义是等价的，如果一个限制注意可控和可观察的代码。
The article reviews different definitions for a convolutional code which can be found in the literature. The algebraic differences between the definitions are worked out in detail. It is shown that bi-infinite support systems are dual to finite-support systems under Pontryagin duality. In this duality the dual of a controllable system is observable and vice versa. Uncontrollability can occur only if there are bi-infinite support trajectories in the behavior, so finite and half-infinite-support systems must be controllable. Unobservability can occur only if there are finite support trajectories in the behavior, so bi-infinite and half-infinite-support systems must be observable. It is shown that the different definitions for convolutional codes are equivalent if one restricts attention to controllable and observable codes.