Puncturing is the predominant strategy to construct high code rate convolutionalencoders, and infinite impulse response (IIR) convolutionalencoders are an essential building block in turbo codes. In this paper, vari...
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Puncturing is the predominant strategy to construct high code rate convolutionalencoders, and infinite impulse response (IIR) convolutionalencoders are an essential building block in turbo codes. In this paper, various properties of convolutionalencoders with these characteristics are developed. In particular, the closed-form representation of a punctured convolutional encoder and its generator matrix is constructed, necessary and sufficient conditions are given such that the puncturedencoders retain the IIR property, and various lower bounds on distance properties, such as effective free distance, are developed. Finally, necessary and sufficient conditions are given on the inverse puncturing problem: representing a known convolutionalencoder as a puncturedencoder.
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