Algebraic aspects of two-dimensional convolutional codes

Two-dimensional (2D) codes are introduced as linear shift-invariant spaces of admissible signals on the discrete plane. Convolutional and, in particular, basic codes are characterized both in terms of their internal properties and by means of their input-output representations. The algebraic structu...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 40; no. 4; pp. 1068 - 1082
Main Authors: Fornasini, E., Valcher, M.E.
Format: Journal Article
Language:English
Published: New York IEEE 01.07.1994
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algebra
Communications
Convolution
Convolutional codes
Data encryption
Decoding
Ear
Inverse problems
Linear systems
Multidimensional systems
Polynomials
State-space methods
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:Two-dimensional (2D) codes are introduced as linear shift-invariant spaces of admissible signals on the discrete plane. Convolutional and, in particular, basic codes are characterized both in terms of their internal properties and by means of their input-output representations. The algebraic structure of the class of all encoders that correspond to a given convolutional code is investigated and the possibility of obtaining 2D decoders, free from catastrophic errors, as,veil as efficient syndrome decoders is considered. Some aspects of the state space implementation of 2D encoders and decoders via (finite memory) 2D system are discussed.< >
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ISSN:0018-9448
1557-9654
DOI:10.1109/18.335967