Dimension/length profiles and trellis complexity of linear block codes

Author

Forney, G. David

Author_Institution

Motorola Inc., Mansfield, MA, USA

Volume

40

Issue

6

fYear

1994

fDate

11/1/1994 12:00:00 AM

Firstpage

1741

Lastpage

1752

Abstract

This semi-tutorial paper discusses the connections between the dimension/length profile (DLP) of a linear code, which is essentially the same as its “generalized Hamming weight hierarchy”, and the complexity of its minimal trellis diagram. These connections are close and deep. DLP duality is closely related to trellis duality. The DLP of a code gives tight bounds on its state and branch complexity profiles under any coordinate ordering; these bounds can often be met. A maximum distance separable (MDS) code is characterized by a certain extremal DLP, from which the main properties of MDS codes are easily derived. The simplicity and generality of these interrelationships are emphasized

Keywords

block codes; computational complexity; linear codes; bounds; branch complexity profiles; coordinate ordering; dimension/length profile; generalized Hamming weight hierarchy; linear block codes; maximum distance separable code; minimal trellis diagram; state complexity profiles; trellis complexity; trellis duality; Block codes; Code standards; Decoding; Hamming distance; Hamming weight; Helium; Information theory; Linear code; State-space methods;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.340452

Filename

340452