Invariancies in punctured convolutional codes-their effect on Viterbi synchronization

This paper studies the invariance of a given punctured convolutional code to an affine class of symbol transformations known to commonly occur in digital transceiver systems. A set of conditions to test the invariance of a code to these transformations has been derived, followed by two proposed methods to compensate for an invariant transformation. The viability of these methods has been examined by doing an invariant factor decomposition on the equivalent code generator matrix (obtained from the original code generator matrix and the given transform). The knowledge of the transformation and the nature of its occurrence greatly determines which method of compensation could be used. This study has much use in not only enabling a code designer to evaluate the invariance of an affine transformation to a given code, but also on the other hand to make the appropriate choice of code generators, puncturing schemes, and bit-to-constellation symbol mapping; so as to allow a channel coding scheme to be either sensitive or invariant to a given transformation, depending upon design objectives.