On locally invertible rate-1/n convolutional encoders

Author

Bitzer, Donald L. ; Dholakia, Ajay ; Koorapaty, Havish ; Vouk, Mladen A.

Author_Institution

Dept. of Comput. Sci., North Carolina State Univ., Raleigh, NC, USA

Volume

44

Issue

1

fYear

1998

fDate

1/1/1998 12:00:00 AM

Firstpage

420

Lastpage

422

Abstract

A locally invertible convolutional encoder has a local inverse defined as a full rank w×w matrix that specifies a one-to-one mapping between equal-length blocks of information and encoded bits. In this correspondence, it is shown that a rate-1/n convolutional encoder is nondegenerate and noncatastrophic if and only if it is locally invertible. Local invertibility is used to obtain upper and lower bounds on the number of consecutive zero-weight branches in a convolutional codeword. Further, existence of a local inverse can be used as an alternate test for noncatastrophicity instead of the usual approach involving computation of the greatest common divisor of n polynomials

Keywords

convolutional codes; inverse problems; matrix inversion; consecutive zero-weight branches; convolutional codeword; local inverse; locally invertible convolutional encoder; lower bounds; noncatastrophic encoder; nondegenerate encoder; rate-1/n convolutional encoder; upper bounds; Automatic repeat request; Convolutional codes; Decoding; Encoding; Error correction; High-speed networks; Testing;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.651074

Filename

651074