Convolutional Decoding in the Presence of Synchronization Errors

We describe the operation of common convolutional decoding algorithms in the presence of insertions, deletions, as well as substitutions in the received message. We first propose a trellis description that can handle the existence of insertions and deletions. Then, we use this trellis diagram to develop the Viterbi algorithm and the Log-MAP algorithm in the presence of synchronization errors. The proposed techniques are presented in the most general form where standard convolutional codes are used and no change to the encoder is required. We establish the effectiveness of the proposed algorithms using standard convolutional codes at different rates.