Punctured recursive convolutional encoders and their applications in turbocodes

Puncturing is the predominant strategy to construct high code rate convolut ional encoders, and infinite impulse response (IIR) convolutional encoders are an essential building block in turbo codes. In this paper, various prop erties of convolutional encoders 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 c onditions are given such that the punctured encoders retain the IIR propert y, and various lower bounds on distance properties, such as effective free distance, are developed. Finally, necessary and sufficient conditions are g iven on the inverse puncturing problem: representing a known convolutional encoder as a punctured encoder.