Syndrome former trellis construction for punctured convolutional codes

In this paper syndrome former trellis construction for punctured convolutional codes (PCCs) is discussed. The class of (n
p
−1)/n
p
-rate PCCs derived from 1/n-rate mother codes is considered. It is shown that a syndrome former trellis of the PCC with identical complexity as the encoder trellis of the mother code can always be constructed. An explicit construction of the syndrome former trellis can be beneficial, when realizing adaptive complexity reduced decoding, or decoding with reduced state transitions, based on the syndrome decoding approach.