Dimension/length profiles and trellis complexity of linear block codes

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...

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Bibliographic Details
Published in:IEEE transactions on information theory 1994-11, Vol.40 (6), p.1741-1752
Main Author: Forney, G.D.
Format: Article
Language:English
Subjects:
Applied sciences
Block codes
Code standards
Coding, codes
Communications
Decoding
Exact sciences and technology
Hamming distance
Hamming weight
Information technology
Information theory
Information, signal and communications theory
Linear code
Signal and communications theory
State-space methods
Telecommunications and information theory
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Summary: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.< >
ISSN:0018-9448
1557-9654
DOI:10.1109/18.340452