Trellis-canonical generator matrices for convolutional codes

2002 ◽  
Author(s):  
Wei Lin ◽  
R.J. McEliece ◽  
Meina Xu
Keyword(s):  
Convolutional Codes ◽  
Canonical Generator ◽  
Generator Matrices

scholarly journals Noncatastrophic convolutional codes over a finite ring

2021 ◽  
Author(s):  
Diego Napp ◽  
Raquel Pinto ◽  
Conceição Rocha
Keyword(s):  
Finite Field ◽  
Convolutional Codes ◽  
Finite Ring ◽  
Important Class ◽  
Finitely Generated ◽  
Polynomial Matrices ◽  
Free Distance ◽  
Generator Matrices

Noncatastrophic encoders are an important class of polynomial generator matrices of convolutional codes. When these polynomials have coefficients in a finite field, these encoders have been characterized as polynomial left prime matrices. In this paper, we study the notion of noncatastrophicity in the context of convolutional codes when the polynomial matrices have entries in the finite ring [Formula: see text]. In particular, we study the notion of zero left prime in order to fully characterize noncatastrophic encoders over the finite ring [Formula: see text]. The second part of the paper is devoted to investigate free and column distance of convolutional codes that are free finitely generated [Formula: see text]-modules. We introduce the notion of [Formula: see text]-degree and provide new bounds on the free distances and column distance. We show that this class of convolutional codes is optimal with respect to the column distance and to the free distance if and only if its projection on [Formula: see text] is.

scholarly journals Minimal and canonical rational generator matrices for convolutional codes

1996 ◽  
Vol 42 (6) ◽  
pp. 1865-1880 ◽  
Author(s):  
G.D. Forney ◽  
R. Johannesson ◽  
Zhe-Xian Wan
Keyword(s):  
Convolutional Codes ◽  
Generator Matrices

Pruned-trellis search technique for high-rate convolutional codes

1989 ◽  
Vol 136 (5) ◽  
pp. 405 ◽  
Author(s):  
J. Sun ◽  
I.S. Reed ◽  
H.E. Huey ◽  
T.K. Truong
Keyword(s):  
Convolutional Codes ◽  
High Rate ◽  
Search Technique

Trap Detection Based Decoding Algorithm for Tail-biting Convolutional Codes

2011 ◽  
Vol 33 (10) ◽  
pp. 2300-2305
Author(s):  
Xiao-tao Wang ◽  
Hua Qian ◽  
Jing Xu ◽  
Yang Yang
Keyword(s):  
Convolutional Codes ◽  
Decoding Algorithm ◽  
Tail Biting
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