Punctured convolutional codes revisited: the exact state diagram and its implications

Accurate analysis of (non-punctured) convolutional codes using the state diagram and transfer function has been well-established; but for punctured convolutional codes, approximation has been the typical treatment This paper discusses a simple way to derive the exact state diagram and transfer function of a punctured convolutional code. The key is to represent the punctured code in an equivalent closed-form. It is shown that such a representation is always possible and that the new code typically has the same or fewer numbers of states. Implications and applications of this finding on performance bounds, puncturing pattern design, decoder implementation for punctured convolutional and punctured turbo codes are also discussed.