Construction of fast recovery codes using a new optimal importance sampling method

We introduce the problem of constructing good fast recovery convolutional codes. When the constraint lengths of the candidate codes are long (say more than 12), it is too computationally complex to perform the code search task. Fortunately, we can transform the code construction problem to a problem related to a transient Markov system. We then develop an optimal importance sampling (IS) method to fulfil the tasks. In this article, we also prove several propositions for optimal IS. For instance, we show analytically that the optimal IS method is unique. We prove that the optimal IS method must converge to the standard Monte Carlo (MC) simulation method when the sample path length approaches infinity. This finding shows that it is not the size of the state space of the Markov system, but the sample path length, that limits the efficiency of the IS method. Based on insights from the optimal IS method, a suboptimal IS method is then proposed to search for long fast recovery codes. The suboptimal method can achieve a substantial speedup gain. After that, several numerical results are presented to study the efficiency of the IS methods and to justify the code search procedures. Finally, we give the code search results and the application of these codes.