Optimal Decoding of Convolutional Codes using a Linear State Space Control Formulation

Abstract

The equivalence of a systematic convolutional encoder as linear state-space control system is first realized and presented through an example. Then, utilizing this structure, a new optimal state-sequence estimator is derived, in the spirit of the Viterbi algorithm. Afterwords, a novel way to perform optimal decoding is achieved, named the Bowyer Decoder, which is a fully deterministic decoder in that the full FSM is known to the decoding algorithm.