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• W1976377399 startingPage "1310" @default.
• W1976377399 abstract "In this paper, exact formulae of the input-output weight distribution function and its exponential growth rate are derived for truncated convolutional encoders. In particular, these weight distribution functions are expressed in terms of generating functions of error events associated with a minimal realization of the encoder. Although explicit analytic expressions can be computed for relatively small truncation lengths, the explicit expressions become prohibitively complex to compute as the truncation lengths and the weights increase. Fortunately, a very accurate asymptotic expansion can be derived using the multidimensional saddle-point method (MSP method). This approximation is substantially easier to evaluate and is used to obtain an expression of the asymptotic spectral function, and to prove continuity and concavity in its domain (convex and closed). Finally, this approach is able to guarantee that the sequence of exponential growth rates converges uniformly to the asymptotic limit, and to estimate the speed of this convergence." @default.
• W1976377399 created "2016-06-24" @default.
• W1976377399 creator A5052019467 @default.
• W1976377399 creator A5066105783 @default.
• W1976377399 date "2012-01-01" @default.
• W1976377399 modified "2023-09-25" @default.
• W1976377399 title "On the Growth Rate of the Input-Output Weight Distribution of Convolutional Encoders" @default.
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• W1976377399 doi "https://doi.org/10.1137/110830307" @default.
• W1976377399 hasPublicationYear "2012" @default.
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