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- W2099060147 abstract "A full-rank K/spl times/n matrix G(D) over the rational functions F(D) generates a rate R=k/n convolutional code C. G(D) is minimal if it can be realized with as few memory elements as any encoder for C, and G(D) is canonical if it has a minimal realization in controller canonical form. We show that G(D) is minimal if and only if for all rational input sequences u(D), the span of u(D)G(D) covers the span of u(D). Alternatively, G(D) is minimal if and only if G(D) is globally zero-free, or globally invertible. We show that G(D) is canonical if and only if G(D) is minimal and also globally orthogonal, in the valuation-theoretic sense of Monna (1970)." @default.
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- W2099060147 date "1996-01-01" @default.
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- W2099060147 title "Minimal and canonical rational generator matrices for convolutional codes" @default.
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- W2099060147 doi "https://doi.org/10.1109/18.556681" @default.
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