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

TL;DR

This paper introduces a novel optimal decoding method for convolutional codes by framing the encoder as a linear state-space control system, leading to the development of the deterministic Bowyer Decoder.

Contribution

It presents the first explicit formulation of convolutional encoding as a linear state-space system and introduces the Bowyer Decoder, a new deterministic decoding algorithm.

Findings

The Bowyer Decoder achieves optimal decoding performance.

The state-space formulation simplifies the decoding process.

The method is fully deterministic, leveraging the complete FSM.

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.