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A convolutional encoder is said to be catastrophic if it maps an informationsequence of infinite weight into a code sequence of finite weight. As aconsequence of this mapping, a finite number of channel errors may cause aninfinite number of information bit errors when decoding. This situation shouldbe avoided. A catastrophic condition to determine if a time-invariantconvolutional encoder is catastrophic or not is stated in \cite{Massey:LSC}.Palazzo developed this condition for periodically time-varying convolutionalencoders in \cite{Palazzo:Analysis}. Since Palazzo's condition is based on thestate transition table of the constituent encoders, its complexity increasesexponentially with the number of memory elements in the encoders. A novelcatastrophic condition making use of time-varying equivalent convolutionalencoders is presented in this letter. A technique to convert a catastrophicperiodically time-varying convolutional encoder into a non-catastrophic one canalso be developed based on these encoders. Since they do not involve the statetransitions of the convolutional encoder, the time complexity of these methodsgrows linearly with the encoder memory.

A Novel Catastrophic Condition for Periodically Time-varying Convolutional Encoders Based on Time-varying Equivalent Convolutional Encoders