Recovery of unknown constraint length and encoder polynomials for rate 1/2 linear convolutional encoders

Abstract

It is sometimes useful to recover convolutionally encoded data without knowing the encoder parameters. The necessary first step is to recover these parameters so that a suitable decoder can be selected. In this study an attempt is made to recover the unknown constraint length K and the convolutional code polynomials for a feedback-free rate 1/2 encoder from a received data stream. It will be shown that the output of such an encoder uniquely characterizes it and permits unambiguous identification of both K and the polynomials if the input data stream is sufficiently exciting and if the received encoded stream is both abundant and is free of transmission error. The encoder output can be collected and collated in a manner that permits synthesis of an impulse response. Even though such an impulse input has not occurred, from the synthesized sequence one may derive the encoder parameters. The application of this synthetic impulse response algorithm with noisy data is then explored, and directions for further research are identified.