1. A trellis processing apparatus for calculating and storing branch metrics in a reduced state trellis, comprising: a processor configured to: calculate, for each trellis state, a sum of products of signal symbol values and channel coefficient values, the channel coefficient values corresponding to delays larger than the maximum value represented by the trellis state, and initialize the branch metrics leading out of each trellis state with the calculated sum of products; and a memory configured to store the products.