Journal ArticleDOI
Structural analysis of convolutional codes via dual codes
TLDR
A linear correspondence is developed between theStates of a rate- k/n convolutional encoder G and the states of a corresponding syndrome former H^T, where H is an encoder of the code dual to the code generated by G .Abstract:
A linear correspondence is developed between the states of a rate- k/n convolutional encoder G and the states of a corresponding syndrome former H^T , where H is an encoder of the code dual to the code generated by G . This correspondence is used to find an expression for the number of all-zero paths of length \tau in the code trellis; the answer depends only on the constraint lengths of the dual code. A partial answer to the resynchronization problem also falls out of this development.read more
Citations
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Journal ArticleDOI
A view of three decades of linear filtering theory
TL;DR: Developments in the theory of linear least-squares estimation in the last thirty years or so are outlined and particular attention is paid to early mathematica[ work in the field and to more modern developments showing some of the many connections between least-Squares filtering and other fields.
Book
Algebraic Codes for Data Transmission
TL;DR: This paper presents codes and algorithms for majority decoding based on the Fourier transform, as well as algorithms based on graphs, for linear block codes and beyond BCH codes.
Journal ArticleDOI
Coset codes. I. Introduction and geometrical classification
TL;DR: The known types of coset codes, as well as a number of new classes that systematize and generalize known codes, are classified and compared in terms of these parameters.
Journal ArticleDOI
Trellis shaping
TL;DR: Trellis shaping, a method of selecting a minimum-weight sequence from an equivalence class of possible transmitted sequences by a search through the trellis diagram of a shaping convolutional code C/sub s/.
Journal ArticleDOI
The dynamics of group codes: state spaces, trellis diagrams, and canonical encoders
G.D. Forney,M.D. Trott +1 more
TL;DR: If C is complete and strongly controllable, then a minimal encoder in controller canonical (feedbackfree) form may be constructed from certain sets of shortest possible code sequences, called granules.
References
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Journal ArticleDOI
Convolutional codes I: Algebraic structure
TL;DR: Minimal encoders are shown to be immune to catastrophic error propagation and, in fact, to lead in a certain sense to the shortest decoded error sequences possible per error event.
Journal ArticleDOI
On the observability of linear, time-invariant systems with unknown inputs
G. Basile,Giovanni Marro +1 more
TL;DR: In this article, the authors considered the observation of linear, time-invariant dynamical systems in the general case in which some of the input functions are unknown and provided a convenient expression for the observability subspace.
Journal ArticleDOI
Structure and stability of discrete-time optimal systems
D. Rappaport,L. Silverman +1 more
TL;DR: In this paper, a complete stability theory for discrete-time linear systems with respect to general quadratic costs, including singular cases, is presented, and several tests for perfect observability are also given.