Bounds for the computation of the free distance of codes based on convolution

This paper presents new bounds to be used in the search for the free distance (D_free) of infinite response codes based on filtering a PAM modulated signal. The bounds extend the two main criteria used to prune paths with trellis codes, namely: path weight comparisons: from each state only the path with the smallest weight is extended; and bounding: if the weight is larger than an upper bound on D _free then no path is extended. If a PAM signal is filtered with an IIR filter, then we have a linear tree code, and the paths do not merge. In addition, the weight D_free is reached only in the limit. We show that, by using more powerful bounds, it is possible to compare paths in the cases of “near merges,” and to find when a path corresponds to D_free in early stages of the search. The new bounds are useful for several types of convolutional coding, and for that reason we present a quite general approach, and exemplify the solutions for filtered PAM and also for binary convolutional codes (BCC)