An analysis of sequential decoding for specific time-invariant convolutional codes

A new analysis of the computational effort and the error probability of sequential decoding is presented, which is based entirely on the distance properties of a particular convolutional code and employs no random-coding arguments. An upper bound on the computational distribution
P(C_{t}>N_{t})
for a specific time-invariant code is derived, which decreases exponentially with the column distance of the code. It is proved that rapid column-distance growth minimizes the decoding effort and therefore also the probability of decoding failure or erasure. In an analogous way, the undetected error probability of sequential decoding with a particular fixed code is proved to decrease exponentially with the free distance and to increase linearly with the number of minimum free-weight codewords. This analysis proves that code construction for sequential decoding should maximize column-distance growth and free distance in order to guarantee fast decoding, a minimum erasure probability, and a low undetected error probability.