We present a novel machine translation model which models translation by a linear sequence of operations. In contrast to the ``N-gram'' model, this sequence includes not only translation but also reordering operations.
Key ideas of our model are (i) a new reordering approach which better restricts the position to which a word or phrase can be moved, and is able to handle short and long distance reorderings in a unified way, and (ii) a joint sequence model for the translation and reordering probabilities which is more flexible than standard phrase-based MT. We observe statistically significant improvements in BLEU over Moses for German-to-English and Spanish-to-English tasks, and comparable results for a French-to-English task.