On the structure of linear recurrent error-control codes
Centre de Mathématiques et Leurs Applications,
École Normale Supérieure de Cachan,
61 avenue du Président Wilson,
2 Laboratoire GAGE, École polytechnique, 91128 Palaiseau, France.
We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.
Mathematics Subject Classification: 93C65 / 94B05 / 94B10 / 12H05 / 13A02 / 13C05
Key words: Convolutional codes / linear recurrent codes / block codes / transducers / encoders / feedback decoding / linear systems / controllability / observability / input-output inversion / modules.
© EDP Sciences, SMAI, 2002