A fast algorithm for computing distance spectrum of convolutional codes

A fast algorithm for searching a tree (FAST) is presented for computing the distance spectrum of convolutional codes. The distance profile of a code is used to limit substantially the error patterns that have to be searched. The algorithm can easily be modified to determine the number of nonzero information bits of an incorrect path as well as the length of an error event. For testing systematic codes, a faster version of the algorithm is given. FAST is much faster than the standard bidirectional search. On a microVAX, d_∞=27 was verified for a rate R=1/2, memory M=25 code in 37 s of CPU time. Extensive tables of rate R=1/2 encoders are given. Several of the listed encoders have distance spectra superior to those of any previously known codes of the same rate and memory. A conjecture than an R=1/2 systematic convolutional code of memory 2M will perform as well as a nonsystematic convolutional code of memory M is given strong support