I've duplicated the algorithm in the text (fig 15.6 in my edition), but this (algorithm, as published) is almost certainly wrong. The forward operation uses the latest (the t-d th would have made more sense) perception. This doesn't make too much sense.
The values don't match up with those generated by the foreward backward implementation (which is almost certainly working correctly).
Need to get the algorithm clarified by Dr N. Incredibly enough, there aren't too many resources online about this particular (variant of the) algorithm .