Code invariances and self-synchronized Viterbi decoding

Synchronization is an important feature in the design of high-speed Viterbi decoders for punctured convolutional codes. Since some punctured codes might show invariance (total or partial) to phase rotations or other transformations, it is difficult to determine their synchronization status using a simple method. Necessary and sufficient conditions for a code to be totally invariant to an affine class of symbol transformations have been derived by A. Mogre et al. (see ibid., vol.48, p.1066-9, 2000) in conjunction with invariance compensation techniques at the receiver. Detection of these invariances is usually achieved based on a synchronization pattern. We propose a method to replace this pattern by a cyclic redundancy check code, since such codes are already present in many communications systems. We also investigate the effects of partial invariances, which can occur in several ways. After deriving some sufficient conditions for a code to exhibit partial invariance, we show that for rate k/n convolutional codes with 2k>n, the types of partial invariances considered have negligible effect on the error performance and, therefore, can be ignored at the receiver.