Parameter Estimation of a Convolutional Encoder from Noisy Observations

We consider the problem of estimating the parameters of a convolutional encoder from noisy data observations, i.e. when encoded bits are received with errors. Reverse engineering of a channel encoder has applications in cryptanalysis when attacking communication systems and also in DNA sequence analysis, when looking for possible error correcting codes in genomes. We present a new iterative, probabilistic algorithm based on the Expectation Maximization (EM) algorithm. We use the concept of log-likelihood ratio (LLR) algebra which will greatly simplify the derivation and interpretation of our final algorithm. We show results indicating the necessary data length and allowed channel error rate for reliable estimation.